8 citations · 31 across the 11 of their papers we have counts for
16 papers
On unification of colored annular sl(2) knot homology
Anna Beliakova, Matthew Hogancamp, Krzysztof Karol Putyra +1
We show that the Khovanov and Cooper-Krushkal models for colored sl(2) homology are equivalent in the case of the unknot, when formulated in the quantum annular Bar-Natan category.…
A proof of Dunfield-Gukov-Rasmussen Conjecture
Anna Beliakova, Krzysztof K. Putyra, Louis-Hadrien Robert +1
In 2005 Dunfield, Gukov and Rasmussen conjectured an existence of the spectral sequence from the reduced triply graded Khovanov-Rozansky homology of a knot to its knot Floer homolo…
Odd two-variable Soergel bimodules and Rouquier complexes
Mikhail Khovanov, Krzysztof Putyra, Pedro Vaz
We consider the odd analogue of the category of Soergel bimodules. In the odd case and already for two variables, the transposition bimodule cannot be merged into the generating So…
Algebraic versus geometric categorification of the~Alexander polynomial: a~spectral sequence
Krzysztof K Putyra, Anna Beliakova, Louis-Hadrien Robert +1
We construct a bigraded spectral sequence from the gl(0)-homology to knot Floer homology. This spectral sequence is of Bockstein type and comes from a subtle manipulation of coeffi…
Odd Khovanov homology for tangles
Grégoire Naisse, Krzysztof Putyra
We extend the covering of even and odd Khovanov link homology to tangles, using arc algebras. For this, we develop the theory of quasi-associative algebras and bimodules graded ove…
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…
Quantum Link Homology via Trace Functor I
Anna Beliakova, Krzysztof Karol Putyra, Stephan Martin Wehrli
Motivated by topology, we develop a general theory of traces and shadows for an endobicategory, which is a~pair: bicategory and endobifunctor $Σ\colon \mathbf C \to\ma…
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…
On a triply graded Khovanov homology
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…
The degenerate distributive complex is degenerate
Jozef H. Przytycki, Krzysztof K. Putyra
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 , th…
Mirror links have dual odd and generalized Khovanov homology
Wojciech Lubawski, Krzysztof K. Putyra
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}…
Separated presentations of modules over pullback rings
Krzysztof K. Putyra
We define pullback and separated presentations of modules over pullback rings, and, if the ring is a pullback of epimorphisms over a semisimple ring, an algorithm reducing such a p…
A 2-category of chronological cobordisms and odd Khovanov homology
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 d…
Torsion in one-term distributive homology
Alissa S. Crans, Józef H. Przytycki, Krzysztof K. Putyra
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.Rour…
Homology of Distributive Lattices
Jozef H. Przytycki, Krzysztof K. Putyra
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 st…
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…