Transverse knots, branched double covers and Heegaard Floer contact invariants

Details Transverse knots, branched double covers and Heegaard Floer contact invariants Transverse knots, branched double covers and Heegaard Floer contact invariants

2004-12-08

arxiv.org/abs/math/0412183v2

J. Symplectic Geom. 4 (2006), no. 2, 149--170

Mathematics

Geometric Topology

Revised the proofs of Theorems 4 and 5 and the statements of Conjecture 1 and Theorem 3. Other minor corrections

Scientific paper

Given a transverse link in the standard contact 3-sphere, 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.

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