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,ϕ), 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.

Added section about Stein-fillings, fixed some references

References in corpus (1)

• Knot concordance and Heegaard Floer homology invariants in branched covers

Cited by in corpus (16)

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• A note on the knot Floer homology of fibered knots
• Colored HOMFLY-PT polynomials of quasi-alternating $3$-braid knots
• An enhanced Euler characteristic of sutured instanton homology
• Classification of torus bundles that bound rational homology circles
• Irreducible 3-manifolds that cannot be obtained by 0-surgery on a knot
• The upsilon invariant at 1 of 3-braid knots
• Torsion in thin regions of Khovanov homology
• Stability and triviality of the transverse invariant from Khovanov homology
• Stein fillable contact 3-manifolds and positive open books of genus one
• Integral left-orderable surgeries on genus one fibered knots
• On the arc index and Turaev genus of a link