Journal of Symplectic Geometry

Transverse knots, branched double covers and Heegaard Floer contact invariants

Olga Plamenevskaya

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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.

Article information

Source
J. Symplectic Geom., Volume 4, Number 2 (2006), 149-170.

Dates
First available in Project Euclid: 5 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsg/1175790955

Mathematical Reviews number (MathSciNet)
MR2275002

Zentralblatt MATH identifier
1131.57017

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 53Dxx: Symplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx] 57M12: Special coverings, e.g. branched 57Rxx: Differential topology {For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimensional manifolds, see 58Bxx}

Citation

Plamenevskaya, Olga. Transverse knots, branched double covers and Heegaard Floer contact invariants. J. Symplectic Geom. 4 (2006), no. 2, 149--170. https://projecteuclid.org/euclid.jsg/1175790955


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