Bordered heegaard floer homology

Robert Lipshitz, Peter S. Ozsvath, Dylan P. Thurston

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

We construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes in two different versions, one of which (type D) is a module over the algebra and the other of which (type A) is an A module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the A tensor product of the type D module of one piece and the type A module from the other piece is HF of the glued manifold. As a special case of the construction, we specialize to the case of three-manifolds with torus boundary. This case can be used to give another proof of the surgery exact triangle for HF . We relate the bordered Floer homology of a three-manifold with torus boundary with the knot Floer homology of a filling.

Original languageEnglish (US)
Pages (from-to)1-294
Number of pages294
JournalMemoirs of the American Mathematical Society
Volume254
Issue number1216
DOIs
StatePublished - Jul 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Extended topological field theory
  • Heegaard floer homology
  • Holomorphic curves
  • Low-dimensional topology
  • Three-manifold topology

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