Work

Odd Khovanov homology and higher representation theory

Year: 2026

Type: article

Abstract: We introduce a super analogue of \mathfrak{gl}_{2} -foams and use it to define an invariant of oriented tangles, shown to coincide with odd Khovanov homology when restricted to links. We then define a supercategorification of the q -Schur algebra of level 2 and realize our construction as a certain super-2-representation. This gives a representation-theoretic construction of odd Khovanov homology, where signs naturally arise as a byproduct of the super-2-categorical structure. In the process, we define a tensor product for chain complexes in super-2-categories, suitably compatible with homotopies. This could be of independent interest.

Source: Quantum Topology

DOI: 10.4171/qt/266

Authors: Léo Schelstraete, Pedro Vaz

Institutions: Max Planck Institute for Mathematics, UCLouvain

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Fonds De La Recherche Scientifique - FNRS

Awards: G2458125085, G4097973904, G8467847575