Appendix: Heegaard Floer Theory

Abstract

The topological description of contact structures as open book decompositions provides the possibility of defining contact invariants which (at least partially) can be computed from surgery diagrams. In this appendix we outline the construction of such invariants — for a complete discussion the reader is referred to the original papers of Ozsváth and Szabó [135, 136, 137, 138]. To set up the stage, first we discuss Ozsváth-Szabó homology groups of oriented, closed 3-manifolds (together with maps induced by oriented cobordisms). The definition of the group HF(Y) for a 3-manifold Y will rely on some standard constructions in Floer homology. After presenting the surgery triangles for this theory, we outline the definition of the contact Ozsváth-Szabó invariants and verify some of the basic properties of this very sensitive invariant. A few model computations are also given.