Bordered invariants from Khovanov homology Article Swipe
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Khovanov homology
Pure mathematics
Homology (biology)
Mathematics
Computer science
Algebra over a field
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Matthew Hogancamp
,
David E. V. Rose
,
Paul Wedrich
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2404.06301
· OA: W4394709577
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2404.06301
· OA: W4394709577
To every compact oriented surface that is composed entirely out of 2-dimensional 0- and 1-handles, we construct a dg category using structures arising in Khovanov homology. These dg categories form part of the 2-dimensional layer (a.k.a. modular functor) of a categorified version of the sl(2) Turaev--Viro topological field theory. As a byproduct, we obtain a unified perspective on several hitherto disparate constructions in categorified quantum topology, including the Rozansky--Willis invariants, Asaeda--Przytycki--Sikora homologies for links in thickened surfaces, categorified Jones--Wenzl projectors and associated spin networks, and dg horizontal traces.
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