#### Volume 16, issue 6 (2016)

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Bordered Heegaard Floer homology and graph manifolds

### Jonathan Hanselman

Algebraic & Geometric Topology 16 (2016) 3103–3166
##### Abstract

We perform two explicit computations of bordered Heegaard Floer invariants. The first is the type $D$ trimodule associated to the trivial ${S}^{1}$–bundle over the pair of pants $\mathsc{P}$. The second is a bimodule that is necessary for self-gluing when two torus boundary components of a bordered manifold are glued to each other. Using the results of these two computations, we describe an algorithm for computing $\stackrel{̂}{HF}$ of any graph manifold.

##### Keywords
Heegaard Floer homology, bordered Floer homology, graph manifolds
##### Mathematical Subject Classification 2010
Primary: 57M27, 57R58
##### Publication
Received: 22 November 2013
Revised: 12 January 2016
Accepted: 27 February 2016
Published: 15 December 2016
##### Authors
 Jonathan Hanselman Department of Mathematics University of Texas at Austin 1 University Station, C1200 Austin, TX 78712 United States