A cylindrical reformulation of Heegaard Floer homology

  title={A cylindrical reformulation of Heegaard Floer homology},
  author={Robert Lipshitz},
  journal={Geometry \& Topology},
  • R. Lipshitz
  • Published 18 February 2005
  • Mathematics
  • Geometry & Topology
We reformulate Heegaard Floer homology in terms of holomorphic curves in the cylindrical manifold U a0;1c R, where U is the Heegaard surface, instead of Sym g .U/. 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 Ozsvath‐Szabo. We… Expand
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