Naturality and Mapping Class Groups in Heegard Floer Homology.

Cover
Title page
Chapter 1. Introduction
1.1. Motivation
1.2. Statement of results
1.3. Outline
Acknowledgements
Chapter 2. Heegaard Invariants
2.1. Sutured manifolds
2.2. Sutured diagrams
2.3. Moves on diagrams and weak Heegaard invariants
2.4. Strong Heegaard invariants
2.5. Construction of the Heegaard Floer functors
Chapter 3. Examples
Chapter 4. Singularities of Smooth Functions
Chapter 5. Generic One- and Two-Parameter Families of Gradients
5.1. Invariant manifolds
5.2. Bifurcations of gradient vector fields on 3-manifolds
5.3. Sutured functions and gradient-like vector fields
Chapter 6. Translating Bifurcations of Gradients to Heegaard Diagrams
6.1. Separability of gradients
6.2. Codimension-0
6.3. Codimension-1: Overcomplete diagrams
6.4. Codimension-1: Ordinary diagrams
6.5. Codimension-1: Converting Heegaard moves to function moves
6.6. Codimension-2
Chapter 7. Simplifying Moves on Heegaard Diagrams
7.1. Codimension-1
7.2. Codimension-2
Chapter 8. Simplifying Handleswaps
Chapter 9. Strong Heegaard Invariants Have No Monodromy
Chapter 10. Heegaard Floer Homology
10.1. Heegaard Floer homology as a weak Heegaard invariant
10.2. Heegaard Floer homology as a strong Heegaard invariant
10.3. Simple handleswap invariance of Heegaard Floer homology
10.4. Proof of Theorem 2.33
Appendix A. The 2-complex of Handleslides
Bibliography
Index
Back Cover.