A bicomplex of Khovanov homology for colored Jones polynomial

TL;DR

This paper constructs a bicomplex framework for categorifying the colored Jones polynomial, advancing the mathematical understanding of knot invariants through homological methods.

Contribution

It introduces a new bicomplex structure for the categorification of the colored Jones polynomial, addressing a problem posed by Beliakova and Wehrli.

Findings

Bicomplex structure successfully categorifies the colored Jones polynomial

Provides a new homological approach to knot invariants

Advances the theoretical framework for quantum knot invariants

Abstract

We construct a bicomplex for the categorification of the colored Jones polynomial. This work is motivated by the problem suggested by Anna Beliakova and Stephan Wehrli who discussed the categorification of the colored Jones polynomial in their paper.