Equivariant annular Khovanov homology

TL;DR

This paper develops an equivariant version of annular Khovanov homology using Frobenius algebra linked to $U(1) imes U(1)$-equivariant cohomology, and introduces an equivariant Temperley-Lieb algebra, enriching the algebraic framework.

Contribution

It introduces a novel equivariant annular Khovanov homology and an associated equivariant Temperley-Lieb algebra, expanding the algebraic tools in knot theory.

Findings

Constructed equivariant annular Khovanov homology.

Defined an equivariant Temperley-Lieb algebra.

Established connections between the algebra and homology.

Abstract

We construct an equivariant version of annular Khovanov homology via the Frobenius algebra associated with $U(1) \times U(1)$-equivariant cohomology of $\mathbb{CP}^1$. Motivated by the relationship between the Temperley-Lieb algebra and annular Khovanov homology, we also introduce an equivariant analogue of the Temperley-Lieb algebra.