Khovanov homology and tight contact structures
arXiv:0802.3835
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 (9)
- Floer homology and knot complements
- Categorification of the Kauffman bracket skein module of I-bundles over surfaces
- Right-veering diffeomorphisms of compact surfaces with boundary II
- On the Khovanov and knot Floer homologies of quasi-alternating links
- Heegaard Floer homologies and contact structures
- On arc index and maximal Thurston-Bennequin number
- On the contact class in Heegaard Floer homology
- Tight contact structures and genus one fibered knots
- On Transverse Knots and Branched Covers