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On the functoriality of
$\mathfrak{sl}_{2}$ tangle homology
Anna Beliakova, Matthew Hogancamp, Krzysztof K Putyra and Stephan M Wehrli |
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Algebraic & Geometric Topology 23 (2023) 1303–1361
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Abstract |
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We construct an explicit equivalence between the (bi)category of 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. |
Keywords
Khovanov homology, tangle homology, web, foam
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Mathematical Subject Classification
Primary: 57K18
Secondary: 18N25
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References |
Publication
Received: 15 February 2021
Revised: 4 August 2021
Accepted: 14 September 2021
Published: 6 June 2023
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Authors |
| Anna Beliakova | |
| Institut für Mathematik Universität Zürich Zürich Switzerland |
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| Matthew Hogancamp | |
| Department of Mathematics Northeastern University Boston, MA United States |
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| Krzysztof K Putyra | |
| Institute for Theoretical
Studies ETH Zürich Zürich Switzerland |
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| Stephan M Wehrli | |
| Mathematics Department Syracuse University Syracuse, NY United States |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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