Geometry & Topology
- Geom. Topol.
- Volume 10, Number 2 (2006), 955-1096.
A cylindrical reformulation of Heegaard Floer homology
We reformulate Heegaard Floer homology in terms of holomorphic curves in the cylindrical manifold , where is the Heegaard surface, instead of . 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.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Lipshitz, Robert. A cylindrical reformulation of Heegaard Floer homology. Geom. Topol. 10 (2006), no. 2, 955--1096. doi:10.2140/gt.2006.10.955. https://projecteuclid.org/euclid.gt/1513799745