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