A cylindrical reformulation of Heegaard Floer homology

2005/02/28 by Robert Lipshitz · 4 citations
Mathematics · #math.SG #math.GT #msc:57R17 #msc:57M27 #msc:57R58

paper · pdf · doi:10.2140/gt.2006.10.955

published as Geom. Topol. 10 (2006) 955-1096 · This is the version published by Geometry & Topology on 9 August 2006

Abstract

We reformulate Heegaard Floer homology in terms of holomorphic curves in the cylindrical manifold Sigma x [0,1] x R, where Sigma is the Heegaard surface, instead of Sym^g(Sigma). 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 dbar-operator in Heegaard Floer homology, and shorten several proofs. After proving invariance, we show that our construction is equivalent to the original construction of Ozsvath-Szabo. 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.

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