Khovanov homology and tight contact structures

Abstract

Using the relation between Khovanov homology and the Heegaard Floer homology of branched double covers, we show how Khovanov homology can be used to establish tightness of branched double covers of certain transverse knots. We give examples of several infinite families of knots whose branched covers are tight for Khovanov-homological reasons, and show that some of these branched covers are not Stein fillable.

All the results of this paper are now subsumed by arXiv:0808.2336, joint with John A. Baldwin

References in corpus (4)

• Floer homology and knot complements
• On the Khovanov and knot Floer homologies of quasi-alternating links
• Heegaard Floer homologies and contact structures
• On Transverse Knots and Branched Covers

Cited by in corpus (1)

• Notes on the Heegaard-Floer Link Surgery Spectral Sequence