An oriented model for Khovanov homology

TL;DR

This paper presents a new oriented model for Khovanov homology that ensures strict functoriality over integers, using an $sl(2)$ state model and TQFT-based boundary operators.

Contribution

It introduces an alternative, oriented presentation of Khovanov homology with strict functoriality over integers, utilizing a novel $sl(2)$ state model and TQFT framework.

Findings

Achieves strict functoriality over integers in Khovanov homology

Defines boundary operators via twisted morphisms in a TQFT setting

Provides a natural, oriented $sl(2)$ state model for links

Abstract

We give an alternative presentation of Khovanov homology of links with strict functoriality result over integers. The construction uses an oriented $sl(2)$ state model allowing a natural definition of the boundary operator as twisted action of morphisms belonging to a TQFT for trivalent graphs and surfaces.