Bordered Heegaard Floer Homology and Graph Manifolds
Author | : Jonathan Hanselman |
Publisher | : |
Total Pages | : |
Release | : 2014 |
ISBN-10 | : OCLC:888357306 |
ISBN-13 | : |
Rating | : 4/5 (06 Downloads) |
Book excerpt: 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.