Computing HF by factoring mapping classes

Abstract

Bordered Heegaard Floer homology is an invariant for 3-manifolds with boundary. In particular, this invariant associates to a handle decomposition of a surface F a differential graded algebra, and to an arc-slide between two handle decompositions, a bimodule over the two algebras. In this paper, we describe these bimodules for arc-slides explicitly, and then use them to give a combinatorial description of HF of a closed 3-manifold, as well as the bordered Floer homology of any 3-manifold with boundary.