Bordered Heegaard Floer homology
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Publication:4645843
DOI10.1090/MEMO/1216zbMATH Open1422.57080arXiv0810.0687OpenAlexW1642974873WikidataQ63285621 ScholiaQ63285621MaRDI QIDQ4645843
Author name not available (Why is that?)
Publication date: 11 January 2019
Published in: (Search for Journal in Brave)
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-infinity module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the A-infinity 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.
Full work available at URL: https://arxiv.org/abs/0810.0687
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