Equivariant Khovanov Homology of Periodic Links

TL;DR

This paper develops an equivariant version of Khovanov homology for periodic links, generalizing previous work, and provides computational tools including a spectral sequence to analyze these homologies.

Contribution

It introduces a new equivariant Khovanov homology theory applicable over any characteristic, extending prior constructions and establishing invariance and computational methods.

Findings

Constructed an equivariant Khovanov homology invariant.

Proved invariance under equivariant isotopies.

Computed homology for torus links T(n,2).

Abstract

The purpose of this paper is to construct and study equivariant Khovanov homology - a version of Khovanov homology theory for periodic links. Since our construction works regardless of the characteristic of the coefficient ring it generalizes a previous construction by Chbili. We establish invariance under equivariant isotopies of links and study algebraic properties of integral and rational version of the homology theory. Moreover, we construct a skein spectral sequence converging to equivariant Khovanov homology and use this spectral sequence to compute, as an example, equivariant Khovanov homology of torus links $T(n,2)$.