#### Volume 18, issue 5 (2014)

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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 $\stackrel{̂}{HF}$ 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
Primary: 57M27
Secondary: 53D40