Bordered Heegaard Floer homology and graph manifolds

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 $\mathcal{P}$. 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 $\widehat{HF}$ of any graph manifold.