Bordered Heegaard Floer Homology And Graph Manifolds

We use the techniques of bordered Heegaard Floer homology to investigate the Heegaard Floer homology of graph manifolds. Bordered Heegaard Floer homology allows us to split a graph manifold into pieces and perform computations for each piece separately. The resulting invariants can then be combined by a simple algebraic procedure to recover HFhat. Graph manifolds by definition decompose into pieces which are S1-bundles over surfaces. This decomposition makes them particularly well suited to the divide-and-conquer techniques of bordered Heegaard Floer homology. In fact, the problem reduces to computing bordered Heegaard Floer invariants of just two pieces. The first invariant is the type D trimodule associated to the trivial S1-bundle over the pair of pants.