Heegaard Floer homology and genus one, one boundary component open books

Abstract

We compute the Heegaard Floer homology of any rational homology 3-sphere with an open book decomposition of the form (T,\phi), where T is a genus one surface with one boundary component. In addition, we compute the Heegaard Floer homology of any T^2-bundle over S^1 with first Betti number equal to one, and we compare our results with those of Lebow on the embedded contact homology of such torus bundles. We use these computations to place restrictions on Stein-filllings of the contact structures compatible with such open books, to narrow down somewhat the class of 3-braid knots with finite concordance order, and to identify all quasi-alternating links with braid index at most 3.Comment: Added section about Stein-fillings, fixed some reference