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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A cylindrical reformulation of Heegaard Floer homology

Robert Lipshitz

Geometry & Topology 10 (2006) 955–1096

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 Symg(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 2000
Primary: 57R17
Secondary: 57R58, 57M27
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
Robert Lipshitz
Department of Mathematics
Stanford University
Stanford, CA 94305-2125
USA