The Blanchet-Khovanov algebras

TL;DR

This paper introduces graded algebras based on Blanchet's singular cobordisms, providing algebraic models using arc diagram combinatorics to enhance the understanding of functorial Khovanov homology.

Contribution

It offers algebraic formulations of Blanchet's cobordism-based algebras through combinatorial arc diagrams, advancing the algebraic understanding of functorial Khovanov homology.

Findings

Algebras constructed from singular cobordisms

Algebraic models using arc diagram combinatorics

Enhanced functoriality in Khovanov homology

Abstract

Blanchet introduced certain singular cobordisms to fix the functoriality of Khovanov homology. In this paper we introduce graded algebras consisting of such singular cobordisms \`a la Blanchet. As the main result we give algebraic versions of these algebras using the combinatorics of arc diagrams.