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pro vyhledávání: '"Alexander N. Shumakovitch"'
Autor:
Alexander N. Shumakovitch
Publikováno v:
Fundamenta Mathematicae. 225:343-364
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c67abf7993544a49a13f1c9abbafca2d
https://doi.org/10.4064/fm225-1-16
https://doi.org/10.4064/fm225-1-16
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::848d588f2788f0f2d5324df5b43d168e
http://arxiv.org/abs/1601.00798
http://arxiv.org/abs/1601.00798
Autor:
Alexander N. Shumakovitch
Publikováno v:
Journal of Knot Theory and Its Ramifications. 16:1403-1412
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::117a08783ed1b0a1529d7100faeda1da
https://doi.org/10.1142/s0218216507005889
https://doi.org/10.1142/s0218216507005889
Autor:
Alexander N. Shumakovitch
Publikováno v:
Topology. 36:449-469
In this paper I present the Vassiliev invariant of degree 2 of a knot as a polynomial of degree 4 in gleams of a shadow presenting the knot. The coefficients of this polynomial involve Strangeness (a numerical characteristic of a generic immersion of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::296039a541eff886011ed7cfac5b4110
https://doi.org/10.1016/0040-9383(96)00004-3
https://doi.org/10.1016/0040-9383(96)00004-3
Autor:
Alexander N. Shumakovitch
Publikováno v:
Progress in Mathematics ISBN: 9780817682767
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.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fc59c99391d6916e0f7b40fc92ff605f
https://doi.org/10.1007/978-0-8176-8277-4_17
https://doi.org/10.1007/978-0-8176-8277-4_17
Autor:
Alexander N. Shumakovitch
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0a4cefc4f265182358b9a2c88e9383a5
http://arxiv.org/abs/1101.5607
http://arxiv.org/abs/1101.5607