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G&T Monographs |
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A cylindrical reformulation of Heegaard Floer homology
Robert Lipshitz
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Geometry & Topology 10 (2006)
955–1096
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Abstract
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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.
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Keywords
Heegaard Floer homology, symplectic field
theory, holomorphic curves, three–manifold
invariants
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Mathematical Subject Classification
Primary: 57R17
Secondary: 57M27, 57R58
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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
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