Volume 18, issue 5 (2014)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Computing $\widehat{\mathit{HF}}$ by factoring mapping classes

Robert Lipshitz, Peter S Ozsváth and Dylan P Thurston

Geometry & Topology 18 (2014) 2547–2681
Abstract

Bordered Heegaard Floer homology is an invariant for 3–manifolds with boundary. In particular, this invariant associates to a handle decomposition of a surface F 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 HF̂ of a closed 3–manifold, as well as the bordered Floer homology of any 3–manifold with boundary.

Keywords
Heegaard Floer homology, mapping class group, arc-slides
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 53D40
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
Authors
Robert Lipshitz
Department of Mathematics
Columbia University
MC 4425
2990 Broadway
New York, NY 10027
USA
Peter S Ozsváth
Department of Mathematics
Columbia University
MC 4425
2990 Broadway
New York, NY 10027
USA
Dylan P Thurston
Department of Mathematics
Columbia University
MC 4425
2990 Broadway
New York, NY 10027
USA