Odd Khovanov homology and higher representation theory

2023/11/24 by Léo Schelstraete, Schelstraete, Léo, Pedro Vaz +1 · 1 citation
Mathematics · Medicine · #Algebraic structures and combinatorial models #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2311.14394

openalex publication_date 2023/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a supercategorification of the q-Schur algebra of level two and an odd analogue of \mathfrakgl₂-foams. Using these constructions, we define a homological invariant of tangles, and show that it coincides with odd Khovanov homology when restricted to links. This gives a representation theoretic construction of odd Khovanov homology. In the process, we define a tensor product on the category of chain complexes in super-2-categories which is compatible with homotopies. This could be of independent interest.

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