Geometry & Topology 10 (2006) 955–1096

DOI: 10.2140/gt.2006.10.955

arXiv: math.SG/0502404

Abstract

We reformulate Heegaard Floer homology in terms of holomorphic curves in the cylindrical manifold Σ×[0,1]×R, where Σ is the Heegaard surface, instead of Sym^g(Σ). We then show that the entire invariance proof can be carried out in our setting. In the process, we derive a new formula for the index of the ∂–operator in Heegaard Floer homology, and shorten several proofs. After proving invariance, we show that our construction is equivalent to the original construction of Ozsváth–Szabó. We conclude with a discussion of elaborations of Heegaard Floer homology suggested by our construction, as well as a brief discussion of the relation with a program of C Taubes.

Keywords

Heegaard Floer homology, symplectic field theory, holomorphic curves, three–manifold invariants

Mathematical Subject Classification

Primary: 57R17

Secondary: 57M27, 57R58

References

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Publication

Received: 14 May 2005
Revised: 9 October 2005
Accepted: 3 January 2006
Published: 9 August 2006
Proposed: Peter Ozsváth
Seconded: John Morgan, Ronald Fintushel

Authors