Some chain maps on Khovanov complexes and Reidemeister moves

TL;DR

This paper introduces specific chain maps between Khovanov complexes that preserve Reidemeister invariance, enhancing the understanding of Khovanov homology's structural properties.

Contribution

It presents new chain maps that commute with homotopy and retraction maps, establishing Reidemeister invariance in Khovanov homology.

Findings

Chain maps commute with homotopy and retraction maps.

Reidemeister invariance of Khovanov homology is maintained.

Provides a framework for understanding invariance in Khovanov complexes.

Abstract

We introduce some chain maps between Khovanov complexes. Each of the chain maps commutes with a chain homotopy map and a retraction maps which obtain a Reidemeister invariance of Khovanov homology.