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math.AT2019★ 5 cited
On the functoriality of sl(2) tangle homology
Anna Beliakova, Matthew Hogancamp, Krzysztof Karol Putyra +1
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 equivalenc…
math.AT2016
Knot invariants arising from homological operations on Khovanov homology
Krzysztof K. Putyra, Alexander N. Shumakovitch
We construct an algebra of non-trivial homological operations on Khovanov homology with coefficients in generated by two Bockstein operations. We use the unified Khov…
math.AT2010★ 7 cited
Cobordisms with chronologies and a generalisation of the Khovanov complex
Krzysztof Putyra
There are two categorifications of the Jones polynomial: "even" discovered by M.Khovanov in 1999 and "odd" dicovered by P.Ozsvath, J.Rasmussen and Z.Szabo in 2007. The first one ca…