Fixing the functoriality of Khovanov homology: a simple approach

TL;DR

This paper presents a straightforward method to ensure the functoriality of Khovanov homology by adjusting signs in the classical framework, simplifying previous algebraic fixes.

Contribution

It introduces a simple, sign-adjustment approach to fix functoriality in Khovanov homology without extending the original theory.

Findings

Successfully fixes functoriality by sign adjustments

Simplifies previous algebraic and conceptual fixes

Maintains classical Khovanov homology structure

Abstract

Khovanov homology is functorial up to sign with respect to link cobordisms. The sign indeterminacy has been fixed by several authors, by extending the original theory both conceptually and algebraically. In this paper we propose an alternative approach: we stay in the classical setup and fix the functoriality by simply adjusting the signs of the morphisms associated to the Reidemeister moves and the Morse moves.