An action of gl(1|1) on odd annular Khovanov homology

TL;DR

This paper introduces an annular variant of odd Khovanov homology that admits a $rak{gl}(1|1)$ action, maintaining invariance under annular Reidemeister moves, thus enriching the algebraic structure of annular link invariants.

Contribution

It defines a new annular odd Khovanov homology with a $rak{gl}(1|1)$ action that is invariant under annular Reidemeister moves, expanding the algebraic framework of link homologies.

Findings

Established an annular odd Khovanov homology theory.

Proved the $rak{gl}(1|1)$ action is preserved under Reidemeister moves.

Enhanced understanding of algebraic structures in annular link invariants.

Abstract

We define an annular version of odd Khovanov homology and prove that it carries an action of the Lie superalgebra $\mathfrak{gl}(1|1)$ which is preserved under annular Reidemeister moves.