Contents

• Contents
• 1. Introduction
• 2. Background Material
  • 1. The case of knots
    • 1.1 Singular knots, the co-differential $\delta$, and finite type invariants
    • 1.2 Constancy conditions, ${\mathcal K}_n/\delta{\mathcal K}_{n+1}$, and chord diagrams
    • 1.3 Integrability conditions, $\ker\delta$, 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 ${\mathcal M}_n/\delta{\mathcal M}_{n+1}$
    • 3.4 Integrability conditions or $\ker\delta$
• 3. The Classification
  • 4. The class of Knotted Objects
    • 4.1 The Order of Braided Objects
    • 4.2 The Order of $1\hookrightarrow 3$ embeddings
  • 5. The class of 3-Manifolds
  • 6. The class of Plane Curves
• Bibliography