Computing HF^ by factoring mapping classes

摘要

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