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Finite Type Invariants by
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Finite Type Invariants by
Contents
Contents
1. Introduction
2. Background Material
1. The case of knots
1.1 Singular knots, the co-differential
, and finite type invariants
1.2 Constancy conditions,
, and chord diagrams
1.3 Integrability conditions,
, lassoing singular points, and four-term relations
1.4 Hutchings' theory of integration
1.5 Summary
2. The General Theory of Finite Type Invariants
2.1 Cubical complexes
2.2 Polynomials on an affine space
3. The case of integral homology spheres
3.1 The definition
3.2 Preliminaries
3.3 Constancy conditions or
3.4 Integrability conditions or
3. The Classification
4. The class of Knotted Objects
4.1 The Order of Braided Objects
4.2 The Order of
embeddings
5. The class of 3-Manifolds
6. The class of Plane Curves
Bibliography
Dror Bar-Natan
2000-03-19