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

@article{Baldwin2008HeegaardFH,
title={Heegaard Floer homology and genus one, one‐boundary component open books},
author={John A. Baldwin},
journal={Journal of Topology},
year={2008},
volume={1}
}
We compute the Heegaard Floer homology of any rational homology 3‐sphere with an open book decomposition of the form (T, ϕ), 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…

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