TY - JOUR
T1 - On the functoriality of sl2 tangle homology
AU - Beliakova, Anna
AU - Hogancamp, Matthew
AU - Putyra, Krzysztof K.
AU - Wehrli, Stephan M.
N1 - Funding Information:
The authors are grateful to the organizers of the program Homology theories in low-dimensional topology in spring 2017 at the Isaac Newton Institute for Mathematical Sciences in Cambridge, where they have started to work on this project. Beliakova and Putyra are supported by the NCCR SwissMAP founded by Swiss National Science Foundation. Wehrli is partially supported by the Simons Foundation (grant 632059 Stephan Wehrli).
Publisher Copyright:
© 2023, Mathematical Sciences Publishers. All rights reserved.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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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U2 - 10.2140/agt.2023.23.1303
DO - 10.2140/agt.2023.23.1303
M3 - Article
AN - SCOPUS:85163162039
SN - 1472-2747
VL - 23
SP - 1303
EP - 1361
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
IS - 3
ER -