Khovanov homology and the slice genus

TL;DR

This paper introduces a new knot invariant s derived from Khovanov homology, proving it is a concordance invariant and providing bounds for the slice genus, leading to a combinatorial proof of the Milnor conjecture.

Contribution

It defines a new invariant s from Khovanov homology and proves its properties, offering a combinatorial proof of the Milnor conjecture.

Findings

s is a concordance invariant

s provides a lower bound for the slice genus

Offers a combinatorial proof of the Milnor conjecture

Abstract

We use Lee's work on the Khovanov homology to define a knot invariant s. We show that s(K) is a concordance invariant and that it provides a lower bound for the slice genus of K. As a corollary, we give a purely combinatorial proof of the Milnor conjecture.