On the functoriality of sl2 tangle homology

Anna Beliakova, Matthew Hogancamp, Krzysztof K. Putyra, Stephan M. Wehrli

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1303-1361
Number of pages59
JournalAlgebraic and Geometric Topology
Issue number3
StatePublished - 2023

ASJC Scopus subject areas

  • Geometry and Topology


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