## Geometry & Topology

### Computing $\widehat{\mathit{HF}}$ by factoring mapping classes

#### 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.

#### Article information

Source
Geom. Topol., Volume 18, Number 5 (2014), 2547-2681.

Dates
Received: 1 July 2011
Revised: 18 September 2013
Accepted: 16 February 2014
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732881

Digital Object Identifier
doi:10.2140/gt.2014.18.2547

Mathematical Reviews number (MathSciNet)
MR3285222

Zentralblatt MATH identifier
1320.57018

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 53D40: Floer homology and cohomology, symplectic aspects

#### Citation

Lipshitz, Robert; Ozsváth, Peter S; Thurston, Dylan P. Computing $\widehat{\mathit{HF}}$ by factoring mapping classes. Geom. Topol. 18 (2014), no. 5, 2547--2681. doi:10.2140/gt.2014.18.2547. https://projecteuclid.org/euclid.gt/1513732881

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