Odd Khovanov homology and higher representation theory
(2023) arXiv — (2023)
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- We define a supercategorification of the q-Schur algebra of level two and an odd analogue of gl2-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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Dos Santos Santana Forte Vaz, P., Schelstraete, L., & et al. (2023). Odd Khovanov homology and higher representation theory. arXiv. Submitted. https://doi.org/10.48550/arXiv.2311.14394 (Original work published 2023)