Khovanov homology of strongly invertible knots and their quotients

TL;DR

This paper introduces spectral sequences connecting Khovanov homology of strongly invertible knots to their quotient knots' annular Khovanov homologies, providing new tools for knot distinction and insights into Heegaard Floer homology.

Contribution

It constructs novel spectral sequences linking different knot homology theories and applies them to distinguish slice disks and analyze branched double covers.

Findings

Spectral sequence relates Khovanov homology to quotient knots' annular Khovanov homologies.

Re-proves that Khovanov homology distinguishes certain slice disks.

Provides an analogous spectral sequence for Heegaard Floer homology.

Abstract

We construct a spectral sequence relating the Khovanov homology of a strongly invertible knot to the annular Khovanov homologies of the two natural quotient knots. Using this spectral sequence, we re-prove that Khovanov homology distinguishes certain slice disks. We also give an analogous spectral sequence for the Heegaard Floer homology of the branched double cover.