Sutured annular Khovanov homology and two periodic braids

TL;DR

This paper establishes a spectral sequence relating the sutured annular Khovanov homology of a two-periodic braid's closure to that of its quotient, revealing structural links in knot invariants.

Contribution

It introduces a spectral sequence connecting the sutured annular Khovanov homologies of two related braids, advancing understanding of periodicity in knot invariants.

Findings

Spectral sequence from two-periodic braid to quotient braid's sutured annular Khovanov homology.

Identification of grading relationships in sutured annular Khovanov homology.

New insights into periodicity effects in knot homology theories.

Abstract

Let $\widetilde{K}$ be a two-periodic braid and let $K$ be its quotient. In this paper we show there is a spectral sequence from the next-to-top winding number grading of the sutured annular Khovanov homology of the closure of $\widetilde{K}$ to the next-to-top winding number grading of the sutured annular Khovanov homology of the closure of $K$.