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Journal of Topology 2008 1(4):963-992; doi:10.1112/jtopol/jtn029
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© 2008 London Mathematical Society

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

John A. Baldwin

Department of Mathematics, Columbia University, New York, NY 10027, USA baldwin@math.columbia.edu


  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 every T2-bundle over S1 with first Betti number equal to 1, 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-fillings 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.

Received May 10, 2008.

2000 Mathematics Subject Classification 57M27, 57R58, 57R17


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