Fixing the functoriality of Khovanov homology: a simple approach

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.

References in corpus (3)

• The universal sl(2) cohomology via webs and foams
• An sl(2) tangle homology and seamed cobordisms
• Khovanov's invariant for closed surfaces

Cited by in corpus (6)

• Categorical lifting of the Jones polynomial: a survey
• Anchored foams and annular homology
• A family of slice-torus invariants from the divisibility of Lee classes
• Homotopy functoriality for Khovanov spectra
• gl(2) foams and the Khovanov homotopy type
• A Bar-Natan homotopy type