Khovanov homology and tight contact structures

TL;DR

This paper demonstrates how Khovanov homology can be used to determine the tightness of branched double covers of transverse knots, providing new examples and insights into contact topology.

Contribution

It introduces a novel method linking Khovanov homology to tight contact structures on branched covers, with explicit examples of infinite families.

Findings

Several infinite families of knots have tight branched covers due to Khovanov homology.

Some of these tight covers are shown to be non-Stein fillable.

The paper establishes a new connection between Khovanov homology and contact topology.

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.