Comultiplicativity of the Ozsv{á}th-Szab{ó} contact invariant
نویسندگان
چکیده
منابع مشابه
Comultiplicativity of the Ozsváth-szabó Contact Invariant
Suppose that S is a surface with boundary and that g and h are diffeomorphisms of S which restrict to the identity on the boundary. Let Yg, Yh, and Yh◦g be the threemanifolds with open book decompositions given by (S, g), (S, h), and (S, h ◦ g), respectively. We show that the Ozsváth-Szabó contact invariant is natural under a comultiplication map μ̃ : d HF (−Yh◦g) → d HF (−Yg)⊗ d HF (−Yh). It fo...
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We use the Ozsváth–Szabó contact invariant to produce examples of strongly symplectically fillable contact 3–manifolds which are not Stein fillable. AMS Classification numbers Primary: 57R17 Secondary: 57R57
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We prove that the Ozsváth-Szabó contact invariant of a closed contact 3manifold with positive 2π–torsion vanishes. In 2002, Ozsváth and Szabó [OSz1] defined an invariant of a closed contact 3-manifold (M, ξ) as an element of the Heegaard Floer homology group ĤF (−M). The definition of the contact invariant was made possible by the work of Giroux [Gi3], which related contact structures and open ...
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Recently, P. Ozsváth and Z. Szabó defined an invariant of contact structures with values in the Heegaard-Floer homology groups. They also proved that the twisted invariant of a weakly symplectically fillable contact structures is non trivial. In this article we prove with an example that their non vanishing result does not hold in general for the untwisted contact invariant. As a consequence of...
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Using the equivalence between the renormalized Euler characteristic of Ozsváth and Szabó, and the Turaev torsion normalized by the Casson-Walker invariant, we make calculations for S p/q(K). An alternative proof of a theorem by Ozsváth and Szabó on L-space surgery obstructions is provided.
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2008
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2008.v15.n2.a6