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Ozsváth-Szabó invariants and fillability of contact structures

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Abstract

Recently Ozsváth and Szabó defined an invariant of contact structures with values in the Heegaard-Floer homology groups. They also proved that a version of the invariant with twisted coefficients is non trivial for weakly symplectically fillable contact structures. In this article we show that their non vanishing result does not hold in general for the contact invariant with untwisted coefficients. As a consequence of this fact Heegaard-Floer theory can distinguish between weakly and strongly symplectically fillable contact structures.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa, largo Pontecorvo 5, I–56127, Pisa, Italy

    Paolo Ghiggini

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  1. Paolo Ghiggini
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Correspondence to Paolo Ghiggini.

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The author is a member of EDGE, Research Training Network HPRN-CT-2000-00101, supported by The European Human Potential Programme.

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Ghiggini, P. Ozsváth-Szabó invariants and fillability of contact structures. Math. Z. 253, 159–175 (2006). https://doi.org/10.1007/s00209-005-0892-8

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  • DOI: https://doi.org/10.1007/s00209-005-0892-8

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