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arXiv · 1903.12194

On the functoriality of sl(2) tangle homology

Anna Beliakova·Matthew Hogancamp·Krzysztof Karol Putyra·Stephan Martin Wehrli
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Abstract

We construct an explicit equivalence between the (bi)category of gl(2) 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 quasi-hereditary 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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Anna Beliakova, Matthew Hogancamp, Krzysztof Karol Putyra, Stephan Martin Wehrli. 2019-03-28. On the functoriality of sl(2) tangle homology. https://doi.org/10.2140/agt.2023.23.1303

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