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Computing
$\widehat{\mathit{HF}}$ by factoring mapping classes
Robert Lipshitz, Peter S Ozsváth and Dylan P Thurston |
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Geometry & Topology 18 (2014) 2547–2681
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Abstract |
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Bordered Heegaard Floer homology is an invariant for –manifolds with boundary. In particular, this invariant associates to a handle decomposition of a surface a differential graded algebra, and to an arc-slide between two handle decompositions, a bimodule over the two algebras. In this paper, we describe these bimodules for arc-slides explicitly, and then use them to give a combinatorial description of of a closed –manifold, as well as the bordered Floer homology of any –manifold with boundary. |
Keywords
Heegaard Floer homology, mapping class group, arc-slides
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Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 53D40
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References |
Publication
Received: 1 July 2011
Revised: 18 September 2013
Accepted: 16 February 2014
Published: 1 December 2014
Proposed: Ronald Fintushel
Seconded: Tomasz Mrowka, Yasha Eliashberg
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Authors |
| Robert Lipshitz | |
| Department of Mathematics Columbia University MC 4425 2990 Broadway New York, NY 10027 USA |
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| Peter S Ozsváth | |
| Department of Mathematics Columbia University MC 4425 2990 Broadway New York, NY 10027 USA |
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| Dylan P Thurston | |
| Department of Mathematics Columbia University MC 4425 2990 Broadway New York, NY 10027 USA |
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