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pro vyhledávání: '"Shumakovitch, Alexander"'
Autor:
Shumakovitch, Alexander N.
We prove that every $\mathbb{Z}_2$H-thin link has no $2^k$-torsion for $k>1$ in its Khovanov homology. Together with previous results by Eun Soo Lee and the author, this implies that integer Khovanov homology of non-split alternating links is complet
Externí odkaz:
http://arxiv.org/abs/1806.05168
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
Externí odkaz:
http://arxiv.org/abs/1601.00798
Autor:
Shumakovitch, Alexander
This is an expository paper discussing various versions of Khovanov homology theories, interrelations between them, their properties, and their applications to other areas of knot theory and low-dimensional topology.
Comment: 24 pages, 15 figure
Comment: 24 pages, 15 figure
Externí odkaz:
http://arxiv.org/abs/1101.5614
Autor:
Shumakovitch, Alexander N.
Publikováno v:
J. Knot Th. and Ramif. 20 (2011) no. 1, 203--222
We investigate properties of the odd Khovanov homology, compare and contrast them with those of the original (even) Khovanov homology, and discuss applications of the odd Khovanov homology to other areas of knot theory and low-dimensional topology. W
Externí odkaz:
http://arxiv.org/abs/1101.5607
Publikováno v:
New York J. Math., 16 (2010) 99-123
Genus 2 mutation is the process of cutting a 3-manifold along an embedded closed genus 2 surface, twisting by the hyper-elliptic involution, and gluing back. This paper compares genus 2 mutation with the better-known Conway mutation in the context of
Externí odkaz:
http://arxiv.org/abs/math/0607258
Autor:
Shumakovitch, Alexander N.
Publikováno v:
J. Knot Th. and Ramif., 16 (2007), no. 10, 1403--1412
We use recently introduced Rasmussen invariant to find knots that are topologically locally-flatly slice but not smoothly slice. We note that this invariant can be used to give a combinatorial proof of the slice-Bennequin inequality. Finally, we comp
Externí odkaz:
http://arxiv.org/abs/math/0411643
Autor:
Shumakovitch, Alexander N.
Publikováno v:
Fund. Math. 225 (2014), 343--364
Khovanov homology is a recently introduced invariant of oriented links in $\mathbb{R}^3$. It categorifies the Jones polynomial in the sense that the (graded) Euler characteristic of the Khovanov homology is a version of the Jones polynomial for links
Externí odkaz:
http://arxiv.org/abs/math/0405474
Autor:
Shumakovitch, Alexander
I present a formula for the Casson invariant of knots associated with divides. The formula is written in terms of Arnold's invariants of pieces of the divide. Various corollaries are discussed.
Comment: 13 pages, 13 figures
Comment: 13 pages, 13 figures
Externí odkaz:
http://arxiv.org/abs/math/0209412
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