Concordance invariants from the $E(-1)$ spectral sequence on Khovanov homology

TL;DR

This paper introduces a new concordance invariant derived from the $E(-1)$ spectral sequence on Khovanov homology, which provides bounds on the nonorientable slice genus of knots.

Contribution

It constructs a novel concordance invariant from the $E(-1)$ spectral sequence, analogous to Rasmussen's $s$ invariant, and demonstrates its application to bounding the nonorientable slice genus.

Findings

The invariant is well-defined and computable.

It provides a bound on the nonorientable slice genus.

The construction parallels Rasmussen's $s$ invariant.

Abstract

We construct the concordance invariant coming from the $E(-1)$ spectral sequence on Khovanov homology in the same way Rasmussen's $s$ invariant comes from the Lee spectral sequence, and show that it gives a bound on the nonorientable slice genus.