Frozen Bibliography of Vassiliev Invariants

Dror Bar-Natan


Date: Jun. 30, 2005; Entries: 576


Department of Mathematics
University of Toronto
Toronto Ontario M5S 3G3
Canada

drorbn@math.toronto.edu

This bibliography is frozen (see Section 5).
An active version is maintained by Sergei Duzhin at http://www.pdmi.ras.ru/~duzhin/VasBib.

This is a partial bibliography of papers on Vassiliev invariants. It aims to be a complete listing of all the papers on the subject, but at this time, it still fails. If your paper (or a paper you are aware of) is omitted (or abused in any other way), it is simply because of the haphazard way by which this bibliography is organized, and not because of a secret plan of mine to ruin your (or anybody else's) reputation. Let me know (please$ \ldots$ I want this bibliography to be as complete as possible!) and it will be fixed. Allow me just one selfish rule: I will not enter any paper into this bibliography unless I have (or I am given) a copy of it.

If you know of hyperlinks to add, please let me know!

Other file formats: pdf ps dvi tex (TeX requires html.sty).

The html version exists in a SPLIT edition for easier browsing, and in a LONG edition for easier searching and printing.

Mikhail Nikolaevitch Goussarov

March 8, 1958 -- June 25, 1999


Contents


List of Additions

This bibliography is frozen (see Section 5).
An active version is maintained by Sergei Duzhin at http://www.pdmi.ras.ru/~duzhin/VasBib.

Following a suggestion by Simon Willerton, here's a list of additions to this bibliography, beyond the first 100 papers (time ordered within each month, but the months are reverse-time-ordered):

Electronic Addresses

This bibliography is frozen (see Section 5).
An active version is maintained by Sergei Duzhin at http://www.pdmi.ras.ru/~duzhin/VasBib.

Here are some author's email, http, and ftp addresses (notice that electronic addresses are constantly changing, so the list below cannot be reliable. Please let me know if you have any additions/corrections). I've started this list before spam went out of control. I feel that the benefit of having it still outweighs the damage it may cause (Some unwanted mass mailing to all who's interested in finite type invariants by some publisher? Unpleasant but we can live with that). However, if you want your name removed please send me a message and I will quickly comply.

Quick Skip Guide: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

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Acknowledgement

This bibliography is frozen (see Section 5).
An active version is maintained by Sergei Duzhin at http://www.pdmi.ras.ru/~duzhin/VasBib.

I wish to thank N. Askitas, S. Duzhin, G. Kuperberg, V. Liskovets, K. Selwat, T. Stanford, A. Stoimenow, D. P. Thurston, A. Vaintrob, and S. Willerton for their comments and suggestions.

Fun mail

This bibliography is frozen (see Section 5).
An active version is maintained by Sergei Duzhin at http://www.pdmi.ras.ru/~duzhin/VasBib.
Here's a fun piece of email I got: (click with no fear, the link is decent)

Date: Sun, 25 Nov 2001 19:51:53 +0000
From: Alexandre Vassiliev <alexandre_vassiliev@hotmail.com>
To: drorbn@math.huji.ac.il
Subject: vassiliev invariants

DEAR SIR
I DO NOT KNOW WHEATHER MY INVARIANTS ARE OK FOR YOU.
LOOK www.vassiliev.com

WARMEST REGARDS
ALEXANDRE VASSILIEV

References


References beginning with A

This bibliography is frozen (see Section 5).
An active version is maintained by Sergei Duzhin at http://www.pdmi.ras.ru/~duzhin/VasBib.

  1. $ \star$ F. Aicardi, Topological invariants of knots and framed knots in the solid torus, to appear in C. R. Ac. Sci. Paris, 1995.

  2. $ \star$ A. K. Aiston, Adams operators and knot decorations, q-alg/9711015 and Liverpool University preprint, November 1997.

  3. $ \star$ P. M. Akhmetiev, On a higher-order analog of the linking number of closed curves, September 1997.

  4. $ \star$ P. M. Akhmetiev and D. Repovs, A generalization of the Sato-Levine invariant, September 1997.

  5. $ \star$ D. Altschuler, Representations of knot groups and Vassiliev invariants, q-alg/9503015 preprint, March 1995.

  6. $ \star$ D. Altschuler and L. Freidel, On universal Vassiliev invariants, hep-th/9403053.

  7. $ \star$ D. Altschuler and L. Freidel, Vassiliev knot invariants and Chern-Simons perturbation theory to all orders, Comm. Math. Phys. 187 (1997) 261-287, arXiv:q-alg/9603010.

  8. $ \star$ M. Alvarez and J. M. F. Labastida, Numerical knot invariants of finite type from Chern-Simons perturbation theory, Nuclear Physics B 433 (1995) 555-596, arXiv:hep-th/9407076.

  9. $ \star$ M. Alvarez and J. M. F. Labastida, Vassiliev invariants for torus knots, Jour. of Knot Theory and its Ramifications 5(6) (1996) 779-803, arXiv:q-alg/9506009.

  10. $ \star$ M. Alvarez and J. M. F. Labastida, Primitive Vassiliev invariants and factorization in Chern-Simons perturbation theory, Comm. Math. Phys. 189-3 (1997), arXiv:q-alg/9604010.

  11. $ \star$ M. Alvarez, J. M. F. Labastida and E. Pérez, Vassiliev invariants for links from Chern-Simons perturbation theory, Nuclear Physics B 488 (1997) 677, arXiv:hep-th/9607030.

  12. $ \star$ J. E. Andersen and J. Mattes, Configuration space integrals and universal Vassiliev invariants over closed surfaces, q-alg/9704019 preprint, April 1997.

  13. $ \star$ J. E. Andersen, J. Mattes and N. Reshetikhin, The poisson structure on the moduli space of flat connections and chord diagrams, Topology 35 (1996) 1069-1083.

  14. $ \star$ J. E. Andersen, J. Mattes and N. Reshetikhin, Quantization of the algebra of chord diagrams, Mathematical Proceedings of the Cambridge Philosophical Society (1998), arXiv:q-alg/9701018

  15. $ \star$ J. E. Andersen and V. Turaev, Higher skein modules, Århus University and MaPhySto preprint, November 1998, arXiv:math.GT/9812071.

  16. $ \star$ E. Appleboim, Finite type invariants of links with fixed linking matrix, Jour. of Knot Theory and its Ramifications, to appear, arXiv:math.GT/9906138.

  17. $ \star$ V. I. Arnold, The Vassiliev theory of discriminants and knots, First European Congress of Mathematics I 3-29, Birkhäuser Basel 1994.

  18. $ \star$ N. A. Askitas, A formula in the theory of finite type invariants, University of Thessaloniki preprint, April 1999,arXiv:math.GT/9904141.

  19. $ \star$ N. A. Askitas and E. Kalfagianni, On knot adjacency, Topology and its Applications 126 (2002) 63-81.

  20. $ \star$ E. Auclair and C. Lescop, Clover calculus for homology 3-spheres via basic algebraic topology, Algebraic and Geometric Topology 5 (2005) 71-106, arXiv:math.GT/0401251.


References beginning with B

This bibliography is frozen (see Section 5).
An active version is maintained by Sergei Duzhin at http://www.pdmi.ras.ru/~duzhin/VasBib.

  1. $ \star$ S. Baader, A note on Vassiliev invariants of quasipositive knots, University of Basel preprint, December 2004, arXiv:math.GT/0412453.

  2. $ \star$ E. Babson, A. Björner, S. Linusson, J. Shareshian and V. Welker, Complexes of not $ i$-connected graphs, Topology 38-2 (1999) 271-299, arXiv:math.CO/9705219.

  3. $ \star$ R. Bacher, Spin models for chord diagrams, Université de Grenoble I preprint, May 1998.

  4. $ \star$ J. C. Baez, Link invariants of finite type and perturbation theory, Lett. Math. Phys. 26 (1992) 43-51, arXiv:hep-th/9207041.

  5. $ \star$ D. Bar-Natan, Weights of Feynman diagrams and the Vassiliev knot invariants, Princeton University preprint, February 1991.

  6. $ \star$ D. Bar-Natan, On the Vassiliev knot invariants, Topology 34 (1995) 423-472.

  7. $ \star$ D. Bar-Natan, Vassiliev homotopy string link invariants, Jour. of Knot Theory and its Ramifications 4 (1995) 13-32.

  8. $ \star$ D. Bar-Natan, Non-associative tangles, in Geometric topology (proceedings of the Georgia international topology conference), (W. H. Kazez, ed.), 139-183, Amer. Math. Soc. and International Press, Providence, 1997.

  9. $ \star$ D. Bar-Natan, Some computations related to Vassiliev invariants, electronic publication (circa 1996), http://www.math.toronto.edu/~drorbn/LOP.html#Computations.

  10. $ \star$ D. Bar-Natan, Vassiliev and quantum invariants of braids, in Proc. of Symp. in Appl. Math. 51 (1996) 129-144, The interface of knots and physics, (L. H. Kauffman, ed.), Amer. Math. Soc., Providence.

  11. $ \star$ D. Bar-Natan, Polynomial invariants are polynomial, Math. Res. Lett. 2 (1995) 239-246. See also q-alg/9606025.

  12. $ \star$ D. Bar-Natan, Lie algebras and the Four Color Theorem, Combinatorica 17-1 (1997) 43-52, arXiv:q-alg/9606016.

  13. $ \star$ D. Bar-Natan, Bracelets and the Goussarov filtration of the space of knots, Invariants of knots and 3-manifolds (Kyoto 2001), Geometry and Topology Monographs 4 1-12, arXiv:math.GT/0111267.

  14. $ \star$ D. Bar-Natan, From astrology to topology via Feynman diagrams and Lie algebras, Rendiconti Del Circolo Matematico Di Palermo Serie II 63 (2000) 11-16.

  15. $ \star$ D. Bar-Natan, Finite type invariants, Toronto University preprint, August 2004, arXiv:math.GT/0408182.

  16. $ \star$ D. Bar-Natan and S. Garoufalidis, On the Melvin-Morton-Rozansky conjecture, Invent. Math. 125 (1996) 103-133.

  17. $ \star$ D. Bar-Natan, S. Garoufalidis, L. Rozansky and D. P. Thurston, Wheels, wheeling, and the Kontsevich integral of the unknot, Israel Journal of Mathematics 119 (2000) 217-237, arXiv:q-alg/9703025.

  18. $ \star$ D. Bar-Natan, S. Garoufalidis, L. Rozansky and D. P. Thurston, The Århus integral of rational homology 3-spheres I: A highly non trivial flat connection on $ S^3$, Selecta Mathematica, New Series 8 (2002) 315-339, arXiv:q-alg/9706004.

  19. $ \star$ D. Bar-Natan, S. Garoufalidis, L. Rozansky and D. P. Thurston, The Århus integral of rational homology 3-spheres II: Invariance and universality, Selecta Mathematica, New Series 8 (2002) 341-371, arXiv:math.QA/9801049.

  20. $ \star$ D. Bar-Natan, S. Garoufalidis, L. Rozansky and D. P. Thurston, The Århus integral of rational homology 3-spheres III: The relation with the Le-Murakami-Ohtsuki invariant, Selecta Mathematica, New Series 10 (2004) 305-324, arXiv:math.QA/9808013.

  21. $ \star$ D. Bar-Natan and R. Lawrence, A Rational Surgery Formula for the LMO Invariant, Israel Journal of Mathematics 140 (2004) 29-60, arXiv:math.GT/0007045.

  22. $ \star$ D. Bar-Natan, T. Q. T. Le and D. P. Thurston, Two applications of elementary knot theory to Lie algebras and Vassiliev invariants, Geometry and Topology 7-1 (2003) 1-31, arXiv:math.QA/0204311.

  23. $ \star$ D. Bar-Natan and A. Stoimenow, The fundamental theorem of Vassiliev invariants, in Proc. of the Århus Conf. Geometry and physics, (J. E. Andersen, J. Dupont, H. Pedersen, and A. Swann, eds.), lecture notes in pure and applied mathematics 184 (1997) 101-134, Marcel Dekker, New-York. See also arXiv:q-alg/9702009.

  24. $ \star$ P. Bellingeri and L. Funar, Braids on surfaces and finite type invariants, Université de Grenoble I and Université de Montpellier II preprint, October 2003, arXiv:math.GT/0309245.

  25. $ \star$ A.-B. Berger and I. Stassen, The skein relation for the $ ({\mathfrak{g}}_2,V)$-link invariant, Comm. Math. Helv. 75-1 (2000) 134-155, arXiv:math.QA/9806136.

  26. $ \star$ A.-B. Berger and I. Stassen, Skein relations for link invariants coming from exceptional Lie algebras, Bern University preprint, September 1998. See also math.QA/9901077.

  27. $ \star$ M. Berger, Hamiltonian dynamics generated by Vassiliev invariants, J. Physics A 34 (2001) 1363-1374.

  28. $ \star$ M. Berger, Topological invariants in braid theory, Letters in Mathematical Physics 55 (2001) 181-192.

  29. $ \star$ J. S. Birman, New points of view in knot theory, Bull. Amer. Math. Soc. 28 (1993) 253-287. See also math.GT/9304209.

  30. $ \star$ J. S. Birman, On the combinatorics of Vassiliev invariants, in Braid groups, knot theory and statistical mechanics II Adv. Ser. Math. Phys. 17 (C. N. Yang and M. L. Ge, eds.), World Scientific, New-Jersey 1994, 1-19.

  31. $ \star$ J. S. Birman, Vassiliev invariants of knots and links: a survey, transparencies and video of MSRI lecture, June 1998.

  32. $ \star$ J. S. Birman and X-S. Lin, Knot polynomials and Vassiliev's invariants, Invent. Math. 111 (1993) 225-270.

  33. $ \star$ J. S. Birman and R. Trapp, Braided Chord Diagrams, Jour. of Knot Theory and its Ramifications 7(1) (1998) 1-22. See also math.GT/9804020.

  34. $ \star$ B. Bollobás and O. Riordan, Linearized chord diagrams and an upper bound for Vassiliev invariants, Jour. of Knot Theory and its Ramifications 9(7) (2000) 847-853.

  35. $ \star$ R. Bott, Configuration spaces and imbedding problems, in Proc. of the Århus Conf. Geometry and physics, (J. E. Andersen, J. Dupont, H. Pedersen, and A. Swann, eds.), lecture notes in pure and applied mathematics 184 (1997) 135-140, Marcel Dekker, New-York.

  36. $ \star$ R. Bott, Configuration space invariants of knots and 3-manifolds, transparencies and video of MSRI lecture, October 1998.

  37. $ \star$ R. Bott and C. Taubes, On the self-linking of knots, Jour. Math. Phys. 35 (1994).

  38. $ \star$ D. J. Broadhurst, Conjectured enumeration of Vassiliev invariants, Open University UK preprint, September 1997, arXiv:q-alg/9709031.

  39. $ \star$ D. J. Broadhurst and D. Kreimer, Feynman diagrams as a weight system: four-loop test of a four-term relation, hep-th/9612011, Open University UK (OUT-4102-66), and Mainz University (MZ-TH/96-37) preprint, November 1996.

  40. $ \star$ R. Budney, J. Conant, K. P. Scannell and D. Sinha, New perspectives on self-linking, to appear in Advances in Mathematics, arXiv:math.GT/0303034.

  41. $ \star$ D. Bullock, C. Frohman and J. Kania-Bartoszynska, Understanding the Kauffman bracket skein module, Jour. of Knot Theory and its Ramifications 8(3) (1999) 265-277, arXiv:q-alg/9604013.

  42. $ \star$ U. Burri, For a fixed Turaev shadow all ``Jones-Vassiliev'' invariants depend polynomially on the gleams, University of Basel preprint, March 1995.

  43. $ \star$ U. Burri, Vassiliev invariants and gleam polynomials, q-alg 9605019 preprint, May 1996.


References beginning with C

This bibliography is frozen (see Section 5).
An active version is maintained by Sergei Duzhin at http://www.pdmi.ras.ru/~duzhin/VasBib.

  1. $ \star$ R. Campoamor-Stursberg and V. O. Manturov, Invariant Tensors Formulae via Chord Diagrams, Universidad Complutense and Moscow State University preprint, May 2005, arXiv:math.GT/0505320.

  2. $ \star$ P. Cartier, Construction combinatoire des invariants de Vassiliev-Kontsevich des n\oeuds, C. R. Acad. Sci. Paris 316 Série I (1993) 1205-1210.

  3. $ \star$ A. S. Cattaneo, Configuration space integrals and invariants for 3-manifolds and knots, Low Dimensional Topology, ed. H. Nencka, Cont. Math. 233, (1999) 153-165, arXiv:math.GT/9912083.

  4. $ \star$ A. S. Cattaneo, P. Cotta-Ramusino, J. Fröhlich and M. Martellini, Topological BF theories in 3 and 4 dimensions, J. Math. Phys. 36 (1995) 6137-6160, arXiv:hep-th/9505027.

  5. $ \star$ A. S. Cattaneo, P. Cotta-Ramusino and R. Longoni, Configuration spaces and Vassiliev classes in any dimension, Algebraic and Geometric Topology 2 (2002) 949-1000, arXiv:math.GT/9910139.

  6. $ \star$ A. S. Cattaneo, P. Cotta-Ramusino and R. Longoni, Algebraic structures on graph cohomology, Universität Zürich-Irchel, Università Degli Studi di Milano and Università di Roma ``La Sapienza'' preprint, July 2003, arXiv:math.GT/0307218.

  7. $ \star$ N. Chbili, On the invariants of lens knots, in Proc. Knots 96 (S. Suzuki, ed.) (1997) 365-375, World Scientific.

  8. $ \star$ V. Chernov, The most refined Vassiliev invariant of degree one of knots and links in $ {\mathbb{R}}^1$-fibrations over a surface, Jour. of Knot Theory and its Ramifications 7(2) (1998) 257-266, arXiv:math.GT/9906137.

  9. $ \star$ V. Chernov, Arnold-type invariants of curves on surfaces, Jour. of Knot Theory and its Ramifications 8(1) (1999) 71-97, arXiv:math.GT/9906125.

  10. $ \star$ V. Chernov, Shadows of wave fronts and Arnold-Bennequin type invariants of fronts on surfaces and orbifolds, Amer. Math. Soc. Transl. 2-190 (1999) 159-184, arXiv:math.GT/9906121.

  11. $ \star$ V. Chernov, Finite order invariants of Legendrian, transverse, and framed knots in contact 3-manifolds, ETH Zürich preprint, July 1999, arXiv:math.SG/9907118.

  12. $ \star$ V. Chernov, Vassiliev invariants of Legendrian, of transverse and framed knots in contact 3-manifolds, Max-Planck-Institut Bonn preprint, April 2000, arXiv:math.SG/0005002.

  13. $ \star$ V. Chernov, Isomorphism of the groups of Vassiliev invariants of Legendrian and of pseudo Legendrian Knots in contact 3-manifolds, Compositio Math., to appear, arXiv:math.GT/0012065.

  14. $ \star$ V. Chernov, The universal order one invariant of framed knots in most $ S^1$-bundles over orientable surfaces, Algebraic and Geometric Topology 3-3 (2003) 89-101, arXiv:math.GT/0209027.

  15. $ \star$ S. V. Chmutov, A proof of the Melvin-Morton conjecture and Feynman diagrams, Jour. of Knot Theory and its Ramifications, 7(1) (1998) 23-40.

  16. $ \star$ S. V. Chmutov, Combinatorial analog of the Melvin-Morton conjecture, Proceedings of KNOTS '96, World Scientific Publishing Co. (1997) 257-266.

  17. $ \star$ S. V. Chmutov and S. V. Duzhin, An upper bound for the number of Vassiliev knot invariants, Jour. of Knot Theory and its Ramifications, 3(2) (1994), 141-151.

  18. $ \star$ S. V. Chmutov and S. V. Duzhin, A lower bound for the number of Vassiliev knot invariants, Topology and Applications 92 (1999) 201-223.

  19. $ \star$ S. V. Chmutov and S. V. Duzhin, The Kontsevich integral, Acta Applicandae Mathematicae 66 (2001) 155-190.

  20. $ \star$ S. V. Chmutov and S. V. Duzhin, CDBook. Introduction to Vassiliev Knot invariants, a preliminary draft version of a book, August 2004.

  21. $ \star$ S. V. Chmutov and S. V. Duzhin, The Kontsevich integral, to appear in the Encyclopedia of Mathematical Physics, Elsevier, arXiv:math.GT/0501040.

  22. $ \star$ S. V. Chmutov, S. V. Duzhin and A. I. Kaishev, The algebra of 3-graphs, Trans. Steklov Math. Institute 221 (1998), 168-196.

  23. $ \star$ S. V. Chmutov, S. V. Duzhin and S. K. Lando, Vassiliev knot invariants I. Introduction, in Adv. in Soviet Math., 21 (1994) Singularities and curves, (V. I. Arnold, ed.), 117-126.

  24. $ \star$ S. V. Chmutov, S. V. Duzhin and S. K. Lando, Vassiliev knot invariants II. Intersection graph conjecture for trees, in Adv. in Soviet Math., 21 (1994) Singularities and curves, (V. I. Arnold, ed.), 127-134.

  25. $ \star$ S. V. Chmutov, S. V. Duzhin and S. K. Lando, Vassiliev knot invariants III. Forest algebra and weighted graphs, in Adv. in Soviet Math., 21 (1994) Singularities and curves, (V. I. Arnold, ed.), 135-145.

  26. $ \star$ S. V. Chmutov and V. Goryunov, Kauffman bracket of plane curves, Comm. Math. Physics 182 (1996) 83-103.

  27. $ \star$ S. V. Chmutov and A. N. Varchenko, Remarks on the Vassilliev knot invariants coming from $ sl_2$, Topology 36-1 (1997).

  28. $ \star$ T. D. Cochran and P. M. Melvin, Finite type invariants of 3-manifolds, Rice University and Bryn Mawr College preprint, November 1997. See also math.GT/9805026.

  29. $ \star$ T. D. Cochran and P. M. Melvin, Quantum cyclotomic orders of 3-manifolds, Rice University and Bryn Mawr College preprint, November 1997. See also math.GT/9809129.

  30. $ \star$ F. .R. Cohen and J. Wu, Braid groups, free groups, and the loop space of the 2-sphere, University of Rochester and National University of Singapore preprint, September 2004, arXiv:math.AT/0409307.

  31. $ \star$ J. Conant, A knot bounding a grope of class $ n$ is $ \lceil\frac{n}{2}\rceil$-trivial, University of California at San Diego preprint, July 1999. See also math.GT/9907158.

  32. $ \star$ J. Conant, On a theorem of Goussarov, Jour. of Knot Theory and its Ramifications 12-1 (2003) 47-52, arXiv:math.GT/0110057.

  33. $ \star$ J. Conant, Vassiliev invariants and embedded gropes, Cornell University preprint, undated.

  34. $ \star$ J. Conant, Gropes and the rational lift of the Kontsevich integral, University of Tennessee preprint, April 2004, arXiv:math.GT/0404270.

  35. $ \star$ J. Conant, Chirality and the Conway polynomial, University of Tennessee preprint, March 2005, arXiv:math.GT/0503648.

  36. $ \star$ J. Conant, R. Schneiderman and P. Teichner, Jacobi identities in low-dimensional topology, University of Tennessee, Courant Institute and University of California at San Diego preprint, January 2004, arXiv:math.GT/0401427.

  37. $ \star$ J. Conant and P. Teichner, Grope cobordism of classical knots, Topology 43-1) (2004) 119-156, arXiv:math.GT/0012118.

  38. $ \star$ J. Conant and P. Teichner, Grope cobordism and Feynman diagrams, Mathematische Annalen 328 (2004) 135-171, arXiv:math.GT/0209075.


References beginning with D

This bibliography is frozen (see Section 5).
An active version is maintained by Sergei Duzhin at http://www.pdmi.ras.ru/~duzhin/VasBib.

  1. $ \star$ O. T. Dasbach, On subspaces of the space of Vassiliev invariants, Düsseldorf University thesis, August 1995.

  2. $ \star$ O. T. Dasbach, A remark on the HOMFLY-Vassiliev invariants, Düsseldorf University preprint, October 1996.

  3. $ \star$ O. T. Dasbach, On the combinatorial structure of primitive Vassiliev invariants II, Jour. Comb. Theory, Ser. A, to appear.

  4. $ \star$ O. T. Dasbach, On the combinatorial structure of primitive Vassiliev invariants III -- a lower bound, Comm. in Cont. Math. 2-4 (2000) 579-590, arXiv:math.GT/9806086.

  5. $ \star$ O. T. Dasbach and X-S. Lin, The Bennequin number of n-trivial closed n-braids is negative, University of California at Riverside preprint, October 2000, arXiv:math.GT/0010278.

  6. $ \star$ C. Day, Vassiliev invariants for links, Univ. of North Carolina at Chapel Hill preprint, 1992.

  7. $ \star$ J. Dean, Many classical knot invariants are not Vassiliev invariants, Jour. of Knot Theory and its Ramifications, 3(1) (1994) 7-9.

  8. $ \star$ C. De Concini and C. Procesi, Hyperplane arrangements and holonomy equations, Selecta Math., to appear.

  9. $ \star$ T. Deguchi and K. Tsurusaki, A statistical study of random knotting using the Vassiliev invariants, Jour. of Knot Theory and its Ramifications 3(3) (1994) 321-353.

  10. $ \star$ T. Deguchi and K. Tsurusaki, Numerical application of knot invariants and universality of random knotting, in Knot theory (V. F. R. Jones, J. Kania-Bartoszynska, J. H. Przytycki, P. Traczyk, and V. G. Turaev, eds.), Banach Center Publications 42 77-85, Warsaw 1998.

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This bibliography is frozen (see Section 5).
An active version is maintained by Sergei Duzhin at http://www.pdmi.ras.ru/~duzhin/VasBib.

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An active version is maintained by Sergei Duzhin at http://www.pdmi.ras.ru/~duzhin/VasBib.

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An active version is maintained by Sergei Duzhin at http://www.pdmi.ras.ru/~duzhin/VasBib.


References beginning with V

This bibliography is frozen (see Section 5).
An active version is maintained by Sergei Duzhin at http://www.pdmi.ras.ru/~duzhin/VasBib.

  1. $ \star$ A. Vaintrob, Vassiliev knot invariants and Lie $ S$-algebras, New Mexico State University preprint, 1994.

  2. $ \star$ A. Vaintrob, Universal weight systems and the Melvin-Morton expansion of the colored Jones knot invariant, q-alg/9605003 and University of Utah preprint, May 1996.

  3. $ \star$ A. Vaintrob, Melvin-Morton conjecture and primitive Feynman diagrams, q-alg/9605028 and University of Utah preprint, May 1996.

  4. $ \star$ V. A. Vassiliev, Cohomology of knot spaces, in Theory of Singularities and its Applications (Providence) (V. I. Arnold, ed.), Amer. Math. Soc., Providence, 1990.

  5. $ \star$ V. A. Vassiliev, Complements of discriminants of smooth maps: topology and applications, Trans. of Math. Mono. 98, Amer. Math. Soc., Providence, 1992.

  6. $ \star$ V. A. Vassiliev, Invariants of knots and complements of discriminants, Developments in Mathematics, the Moscow School (V. I. Arnold and M. Monastyrsky, eds.), Chapman & Hall, London 1993.

  7. $ \star$ V. A. Vassiliev, On the spaces of polynomial knots, q-alg/9505008 and Independent Moscow University preprint, May 1995.

  8. $ \star$ V. A. Vassiliev, On invariants and homology of spaces of knots in arbitrary manifolds, in Topics in quantum groups and finite-type invariants, (B. Feigin and V. Vassiliev, eds.) AMS Translations Ser. 2 vol. 185 (1998) 155-182, Providence.

  9. $ \star$ V. A. Vassiliev, Homology of $ i$-connected graphs and invariants of knots, plane arrangements, etc., in The Arnoldfest, proceedings of a conference in honour of V. I. Arnold for his sixtieth birthday (E. Bierstone, B. Khesin, A. Khovanskii and J. E. Marsdeneds.), Fields Inst. Comm. 24 (1999) 451-469.

  10. $ \star$ V. A. Vassiliev, On combinatorial formulas for cohomology of spaces of knots, Independent Moscow University preprint, September 2000.

  11. $ \star$ V. V. Vershinin, On Vassiliev invariants for links in handlebodies, Jour. of Knot Theory and its Ramifications 7(5) (1998) 701-712. See also q-alg/9709017.

  12. $ \star$ O. Viro, Self-linking number of a real algebraic link, Uppsala University preprint, July 1995, arXiv:alg-geom/9410030.

  13. $ \star$ O. Viro, Encomplexing the writhe, Uppsala University and POMI St. Petersburg preprint, May 2000, arXiv:math.AG/0005162.

  14. $ \star$ P. Vogel, Invariants de Vassiliev des n\oeuds [d'après D. Bar-Natan, M. Kontsevich et V. A.Vassiliev], Séminaire Bourbaki 761 (1993) 1-17 (also, Asterisque 216 (1993) 213-232).

  15. $ \star$ P. Vogel, Algebraic structures on modules of diagrams, Université Paris VII preprint, July 1995 (revised 1997).

  16. $ \star$ P. Vogel, Vassiliev theory, Université Paris VII preprint, July 1999.

  17. $ \star$ P. Vogel, The universal Lie algebra, Université Paris VII preprint, June 1999.

  18. $ \star$ P. Vogel, Invariants de type fini, in Nouveaux invariants en géométrie et en topologie (François Dumas, Jean-Yves Le Dimet and Sylvie Paycha, eds.), Panor. Synthèses 11 99-128, Soc. Math. France, Paris 2001.

  19. $ \star$ P. Vogel, Vassiliev theory and the universal Lie algebra, Université Paris VII preprint, 2000.

  20. $ \star$ I. Volic, Finite type knot invariants and calculus of functors, Ph.D. thesis, Brown University, 2003, arXiv:math.AT/0401440.

  21. $ \star$ I. Volic, Configuration space integrals and Taylor towers for spaces of knots, University of Virginia preprint, January 2004, arXiv:math.GT/0401282.

  22. $ \star$ I. Volic, A survey of Bott-Taubes integration, University of Virginia preprint, February 2005, arXiv:math.GT/0502295.


References beginning with W

This bibliography is frozen (see Section 5).
An active version is maintained by Sergei Duzhin at http://www.pdmi.ras.ru/~duzhin/VasBib.

  1. $ \star$ S. Willerton, Vassiliev invariants and the Hopf algebra of chord diagrams, Math. Proc. Camb. Phil. Soc. 119 (1996) 55-65.

  2. $ \star$ S. Willerton, A topological tie-in, Nature 368 No. 6467 (1994) 103-104.

  3. $ \star$ S. Willerton, A combinatorial half-integration from weight system to Vassiliev knot invariant, Jour. of Knot Theory and its Ramifications 7(4) (1998) 519-526.

  4. $ \star$ S. Willerton, Vassiliev invariants as polynomials, in Knot theory (V. F. R. Jones, J. Kania-Bartoszynska, J. H. Przytycki, P. Traczyk, and V. G. Turaev, eds.), Banach Center Publications 42 457-463, Warsaw 1998.

  5. $ \star$ S. Willerton, On the Vassiliev invariants for knots and for pure braids, Ph.D. thesis, University of Edinburgh.

  6. $ \star$ S. Willerton, Fishing with Vassiliev invariants, web document, http://www.sheffield.ac.uk/simonwillerton/fishing.html.

  7. $ \star$ S. Willerton, The Kontsevich integral and algebraic structures on the space of diagrams, Knots in Hellas '98, Knots and Everything 24, World Scientific 2000, 530-546, arXiv:math.GT/9909151.

  8. $ \star$ S. Willerton, On the first two Vassiliev invariants, IRMA Strasbourg preprint, March 1999, arXiv:math.GT/0104061.

  9. $ \star$ S. Willerton, An almost-integral universal Vassiliev invariant of knots, Algebraic and Geometric Topology 2-29 (2002) 649-664, arXiv:math.GT/0105190.


References beginning with X

This bibliography is frozen (see Section 5).
An active version is maintained by Sergei Duzhin at http://www.pdmi.ras.ru/~duzhin/VasBib.


References beginning with Y

This bibliography is frozen (see Section 5).
An active version is maintained by Sergei Duzhin at http://www.pdmi.ras.ru/~duzhin/VasBib.

  1. $ \star$ H. Yamada, Delta distance and Vassiliev invariants of knots, Jour. of Knot Theory and its Ramifications 9(7) (2000) 967-974.

  2. $ \star$ S.-W. Yang, Feynman integral, knot invariant and degree theory of maps, National Taiwan University preprint, September 1997, arXiv:q-alg/9709029.

  3. $ \star$ A. Yasuhara, $ C_k$-moves on spatial theta-curves and Vassiliev invariants, George Washington University preprint, April 2001, arXiv:math.GT/0104177.

  4. $ \star$ A. Yasuhara, Brunnian local moves of knots and Vassiliev invariants, Tokyo Gakugei University preprint, December 2004, arXiv:math.GT/0412489.

  5. $ \star$ D. N. Yetter, Braided deformations of monoidal categories and Vassiliev invariants Kansas State University preprint, October 1997. See also q-alg/9710010.


References beginning with Z

This bibliography is frozen (see Section 5).
An active version is maintained by Sergei Duzhin at http://www.pdmi.ras.ru/~duzhin/VasBib.

  1. $ \star$ D. Zagier, Vassiliev invariants and a strange identity related to the Dedekind eta-function, Topology 40(5) (2001) 945-960.

  2. $ \star$ J. Zhu, On singular braids, Jour. of Knot Theory and its Ramifications 6(3) (1997) 427-440.

  3. $ \star$ J. Zhu, On Jones knot invariants and Vassiliev invariants, New Zealand Jour. of Math., to appear.


Notice of Retirement

Exactly 10 years since the beginning of the ``List of Additions'' in Section 1, on June 30, 2005, I have stopped updating this bibliography.

Sergei Duzhin continues to update his version of this bibliography. Visit it at

http://www.pdmi.ras.ru/~duzhin/VasBib.

The full source files for my (frozen) version are at

http://www.math.toronto.edu/~drorbn/VasBib/VasBib.tar.gz.

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Frozen Bibliography of Vassiliev Invariants

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