# Khovanov homology and periodic links

## TL;DR

This paper introduces an equivariant version of Khovanov, Lee, and Bar-Natan homologies for periodic links, establishing a spectral sequence that provides new obstructions to a link's periodicity, extending prior results.

## Contribution

It defines an equivariant homology framework for periodic links and constructs a spectral sequence linking these homologies, offering novel tools for detecting link periodicity.

## Key findings

- Existence of an equivariant spectral sequence from Khovanov to Lee homology for periodic links
- New obstructions for determining link periodicity
- Generalization of previous periodicity obstructions by Przytycki and the second author

## Abstract

Based on the results of the second author, we define an equivariant version of Lee and Bar-Natan homology for periodic links and show that there exists an equivariant spectral sequence from the equivariant Khovanov homology to equivariant Lee homology. As a result we obtain new obstructions for a link to be periodic. These obstructions generalize previous results of Przytycki and of the second author.