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June 2006 Transverse knots, branched double covers and Heegaard Floer contact invariants
Olga Plamenevskaya
J. Symplectic Geom. 4(2): 149-170 (June 2006).

Abstract

Given a transverse link in $(S\sp {3} , \xi\sb {std})$, we study the contact manifold that arises as a branched double cover of the sphere. We give a contact surgery description of such manifolds, which allows to determine the Heegaard Floer contact invariants for some of them. By example of the knots of Birman–Menasco, we show that these contact manifolds may fail to distinguish between non-isotopic transverse knots. We also investigate the relation between the Heegaard Floer contact invariants of the branched double covers and the Khovanov homology, in particular, the transverse link invariant we introduce in a related paper.

Citation

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Olga Plamenevskaya. "Transverse knots, branched double covers and Heegaard Floer contact invariants." J. Symplectic Geom. 4 (2) 149 - 170, June 2006.

Information

Published: June 2006
First available in Project Euclid: 5 April 2007

zbMATH: 1131.57017
MathSciNet: MR2275002

Subjects:
Primary: 57M25
Secondary: 53Dxx, 57M12, 57Rxx

Rights: Copyright © 2006 International Press of Boston

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Vol.4 • No. 2 • June 2006
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