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Travel prevented by the homeopathic
ash cloud, talk given in Goettingen,
Talk in Luminy, April 2010
I will give the talk on the left and the talk on the right will be
on the back side of the handout.
I will state 18=3x3x2 "fundamental" conjectures on finite type invariants of
various classes of virtual knots. This done, I will state a few further
conjectures about these conjectures and ask a few questions about how these 18
conjectures may or may not interact.
See also Some Dimensions of
Spaces of Finite Type Invariants of Virtual Knots, with Halacheva,
Leung, and Roukema.
w-Knots, from Z to A
I will define w-knots, a class of knots wider than ordinary knots
but weaker than virtual knots, and show that it is quite easy to
construct a universal finite invariant Z of w-knots. In order
to study Z we will introduce the "Euler Operator" and the
"Infinitesimal Alexander Module", at the end finding a simple determinant
formula for Z. With no doubt that formula computes the Alexander
polynomial A, except I don't have a proof yet.
See also Finite Type Invariants of
w-Knotted Objects: From Alexander to Kashiwara and Vergne.
Handout. 18C.html, 18C.pdf.
Talk Video (in Goettingen).
Handout. Z2A.html, Z2A.pdf.
Talk Video: Part
II (in Toronto).
All sources are in Luminy-1004.zip.