# Khovanov homology and periodic links

@article{Borodzik2017KhovanovHA, title={Khovanov homology and periodic links}, author={Maciej Borodzik and Wojciech Politarczyk}, journal={arXiv: Geometric Topology}, year={2017} }

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.

## 6 Citations

Khovanov homotopy type and periodic links

- Mathematics
- 2018

Given an $m$-periodic link $L\subset S^3$, we show that the Khovanov spectrum $\X_L$ constructed by Lipshitz and Sarkar admits a group action. We relate the Borel cohomology of $\X_L$ to the…

A new polynomial criterion for periodic knots

- Mathematics
- 2020

The purpose of this paper is to present a new periodicity criterion. For that purpose, we study the HOMFLY-PT polynomial and the Kauffman polynomial of cables of periodic links. Furthermore, we…

On the groups of periodic links

- Mathematics
- 2018

It is shown that, if a link $\tilde{L}\subset S^3$ is $p^k$-periodic with $p$ prime and $k\ge 1$, and $L$ is the quotient link, then the groups of $\tilde{L}$ and $L$ can be related by counting…

Finite orthogonal groups and periodicity of links

- Mathematics
- 2018

For a prime number $q\neq 2$ and $r>0$ we study, whether there exists an isometry of order $q^r$ acting on a free $\mathbb{Z}_{p^k}$-module equipped with a scalar product. We investigate, whether…

A rank inequality for the annular Khovanov homology of 2-periodic links

- Mathematics
- 2017

For a 2-periodic link $\tilde L$ in the thickened annulus and its quotient link $L$, we exhibit a spectral sequence with $E^1 \cong AKh(\tilde L) \otimes_{\mathbb{F}_2} \mathbb{F}_2[\theta,…

Khovanov homotopy type, periodic links and localizations

- Medicine, MathematicsMathematische annalen
- 2021

By applying the Dwyer–Wilkerson theorem, Khovanov homology of the quotient link is expressed in terms of equivariant Khovanova homological of the original link.

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