On the functoriality of sl₂ tangle homology
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Date
2023
Publication Type
Journal Article
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Abstract
We construct an explicit equivalence between the (bi)category of gl₂ webs and foams and the Bar-Natan (bi)category of Temperley–Lieb diagrams and cobordisms. With this equivalence we can fix functoriality of every link homology theory that factors through the Bar-Natan category. To achieve this, we define web versions of arc algebras and their quasihereditary covers, which provide strictly functorial tangle homologies. Furthermore, we construct explicit isomorphisms between these algebras and the original ones based on Temperley–Lieb cup diagrams. The immediate application is a strictly functorial version of the Beliakova–Putyra–Wehrli quantization of the annular link homology.
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published
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23 (3)
Pages / Article No.
1303 - 1361
Publisher
Mathematical Sciences Publishers
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Subject
Khovanov homology; tangle homology; web; foam