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1. The case of
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Finite Type Invariants by
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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
3.2.1 Surgery and the Kirby calculus
3.2.2 The Borromean rings
3.2.3 The triple linking numbers
3.3 Constancy conditions or
3.3.1 Statement of the result
3.3.2 On a connected space, polynomials are determined by their values at any given point
3.3.3 Homotopy invariance and pure braids
3.3.4 The mask and the interchange move
3.3.5 Reducing third commutators
3.4 Integrability conditions or
3.4.1 +1 and -1 surgeries are opposites
3.4.2 A total twist is a composition of many little ones
3.4.3 The two ways of building an interchange
3.4.4 Lassoing a Borromean link and the IHX relation
Dror Bar-Natan
2000-03-19