Bordered Heegaard Floer homology

@article{Lipshitz2018BorderedHF,
  title={Bordered Heegaard Floer homology},
  author={Robert Lipshitz and Peter S. Ozsvath and Dylan Thurston},
  journal={Memoirs of the American Mathematical
                Society},
  year={2018}
}
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-infinity module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the A-infinity… Expand
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