On the functoriality of sl(2) tangle homology

Algebr. Geom. Topol. 23 (2023) 1303-1361 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 t...

Full description

Saved in:

Bibliographic Details
Main Authors:	Beliakova, Anna, Hogancamp, Matthew, Putyra, Krzysztof Karol, Wehrli, Stephan Martin
Format:	Journal Article
Language:	English
Published:	02-04-2019
Subjects:	Mathematics - Algebraic Topology Mathematics - Quantum Algebra Mathematics - Representation Theory
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	Algebr. Geom. Topol. 23 (2023) 1303-1361 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.
DOI:	10.48550/arxiv.1903.12194