Zobrazeno 1 - 8
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pro vyhledávání: '"Krzysztof K. Putyra"'
Publikováno v:
Inventiones mathematicae. 215:383-492
Motivated by topology, we develop a general theory of traces and shadows for an endobicategory, which is a pair: bicategory and endobifunctor . For a graded linear bicategory and a fixed invertible parameter q, we quantize this theory by using the en
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::362d3d5b5725580e5186471f24f49409
https://doi.org/10.1007/s00222-018-0830-0
https://doi.org/10.1007/s00222-018-0830-0
Publikováno v:
European Journal of Mathematics. 2:993-1012
We prove that the degenerate part of the distributive homology of a multispindle is determined by the normalized homology. In particular, when the multispindle is a quandle Q, the degenerate homology of Q is completely determined by the quandle homol
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https://doi.org/10.1007/s40879-016-0116-2
https://doi.org/10.1007/s40879-016-0116-2
We construct an algebra of non-trivial homological operations on Khovanov homology with coefficients in $\mathbb Z_2$ generated by two Bockstein operations. We use the unified Khovanov homology theory developed by the first author to lift this algebr
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::848d588f2788f0f2d5324df5b43d168e
http://arxiv.org/abs/1601.00798
http://arxiv.org/abs/1601.00798
Autor:
Krzysztof K. Putyra
Cobordisms are naturally bigraded and we show that this grading extends to Khovanov homology, making it a triply graded theory. Although the new grading does not make the homology a stronger invariant, it can be used to show that odd Khovanov homolog
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e4155e581643981a87beb71684877d86
http://arxiv.org/abs/1501.05293
http://arxiv.org/abs/1501.05293
Autor:
Krzysztof K. Putyra, Wojciech Lubawski
Publikováno v:
Algebr. Geom. Topol. 16, no. 4 (2016), 2021-2044
We show that the generalized Khovanov homology, defined by the second author in the framework of chronological cobordisms, admits a grading by the group $\mathbb{Z}\times\mathbb{Z}_2$, in which all homogeneous summands are isomorphic to the unified K
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d86f4a7cf6455ad552ce200008da9654
http://arxiv.org/abs/1407.5987
http://arxiv.org/abs/1407.5987
Autor:
Krzysztof K. Putyra
We create a framework for odd Khovanov homology in the spirit of Bar-Natan's construction for the ordinary Khovanov homology. Namely, we express the cube of resolutions of a link diagram as a diagram in a certain 2-category of chronological cobordism
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http://arxiv.org/abs/1310.1895
http://arxiv.org/abs/1310.1895
The one-term distributive homology was introduced by J.H.Przytycki as an atomic replacement of rack and quandle homology, which was first introduced and developed by R.Fenn, C.Rourke and B.Sanderson, and J.S.Carter, S.Kamada and M.Saito. This homolog
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a89723c0f441cbcf9a632e1055c0fb84
We outline the theory of sets with distributive operations: multishelves and multispindles, with examples provided by semi-lattices, lattices and skew lattices. For every such a structure we define multi-term distributive homology and show some of it
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0f02dc1cc2c988828c95cc3c11309967
http://arxiv.org/abs/1111.4772
http://arxiv.org/abs/1111.4772