Geometry & Topology

A cylindrical reformulation of Heegaard Floer homology

Robert Lipshitz

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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.

Article information

Geom. Topol., Volume 10, Number 2 (2006), 955-1096.

Received: 14 May 2005
Revised: 9 October 2005
Accepted: 3 January 2006
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R17: Symplectic and contact topology
Secondary: 57R58: Floer homology 57M27: Invariants of knots and 3-manifolds

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


Lipshitz, Robert. A cylindrical reformulation of Heegaard Floer homology. Geom. Topol. 10 (2006), no. 2, 955--1096. doi:10.2140/gt.2006.10.955.

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