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Найдено 18 публикаций
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Статья
Deviatov R. Journal of Knot Theory and Its Ramifications. 2009. Vol. 18. No. 9. P. 1193-1203.
Добавлено: 28 июня 2012
Статья
Lightfoot A. C. Journal of Knot Theory and Its Ramifications. 2017. Vol. 26. No. 750077. P. 1-35.
Добавлено: 16 октября 2017
Статья
A.V.Omelchenko, Bogdanov A., Meshkov V. et al. Journal of Knot Theory and Its Ramifications. 2012. Vol. 21. No. 7. P. 1-17.
Добавлено: 30 августа 2018
Статья
V.A. Vassiliev, Grishanov S. Journal of Knot Theory and Its Ramifications. 2011. Vol. 20. No. 03. P. 371-387.
Добавлено: 30 декабря 2017
Статья
Grishanov S. A., Vasiliev V. Journal of Knot Theory and Its Ramifications. 2011. Vol. 20. No. 3. P. 371-387.
Добавлено: 19 декабря 2012
Статья
Victor A. Vassiliev. Journal of Knot Theory and Its Ramifications. 1997. Vol. 6. No. 1. P. 115-123.
Добавлено: 28 мая 2010
Статья
Manturov V., Nikonov I. M. Journal of Knot Theory and Its Ramifications. 2016. Vol. 24. No. 13. P. 1541003-1-1541003-17.

We modify the definition of the Khovanov complex for oriented links in a thickening of an oriented surface to obtain a triply graded homological link invariant with a new homotopical grading.

Добавлено: 5 декабря 2016
Статья
Mironov A., Morozov A., Natanzon S. M. Journal of Knot Theory and Its Ramifications. 2014. Vol. 23. No. 6. P. 1-16.

The classical Hurwitz numbers of degree n together with the Hurwitz numbers of the seamed surfaces of degree n give rise to the Klein topological field theory. We extend this construction to the Hurwitz numbers of all degrees at once. The corresponding Cardy-Frobenius algebra is induced by arbitrary Young diagrams and arbitrary bipartite graphs. It turns out to be isomorphic to the algebra of differential operators from [18] which serves a model for open-closed string theory. The operator associated with the Young diagram of the transposition of two elements coincides with the cut-and-join operator which gives rise to relations for the classical Hurwitz numbers. We prove that the operators corresponding to arbitrary Young diagrams and bipartite graphs also give rise to relations for the Hurwitz numbers.

Добавлено: 2 апреля 2014
Статья
Grishanov S. A., Vasiliev V. Journal of Knot Theory and Its Ramifications. 2011. Vol. 20. No. 3. P. 345-370.
Добавлено: 19 декабря 2012
Статья
V.A. Vassiliev, Grishanov S. Journal of Knot Theory and Its Ramifications. 2011. Vol. 20. No. 3. P. 345-370.
Добавлено: 30 декабря 2017
Статья
Omelchenko A., Grishanov S., Meshkov V. Journal of Knot Theory and Its Ramifications. 2007. Vol. 16. No. 6. P. 779-788.
Добавлено: 11 сентября 2018
Статья
Victor A. Vassiliev. Journal of Knot Theory and Its Ramifications. 2016. Vol. 25. No. 12.

The construction of integer linking numbers of closed curves in a three-dimensional manifold usually appeals to the orientation of this manifold. We discuss how to avoid it constructing similar homotopy invariants of links in non-orientable manifolds. 

Добавлено: 15 ноября 2016
Статья
Lightfoot A. C. Journal of Knot Theory and Its Ramifications. 2016. Vol. 25. No. 11. P. 1-18.
Добавлено: 7 ноября 2016
Статья
V.A. Vassiliev, S.A. Grishanov, V.R. Meshkov. Journal of Knot Theory and Its Ramifications. 2009. Vol. 18. No. 2. P. 209-235.
Добавлено: 20 января 2010
Статья
Smirnov E., Kleptsyn V. Journal of Knot Theory and Its Ramifications. 2016. Vol. 26. P. 1642006.

 To each ribbon graph we assign a so-called L-space, which is a Lagrangian subspace in an even-dimensional vector space with the standard symplectic form. This invariant generalizes the notion of the intersection matrix of a chord diagram. Moreover, the actions of Morse perestroikas (or taking a partial dual) and Vassiliev moves on ribbon graphs are reinterpreted nicely in the language of L-spaces, becoming changes of bases in this vector space. Finally, we define a bialgebra structure on the span of L-spaces, which is analogous to the 4-bialgebra structure on chord diagrams.

 

Добавлено: 15 января 2016
Статья
Kalinin N., Shkolnikov M. Journal of Knot Theory and Its Ramifications. 2016. Vol. 25. No. 12. P. 1-12.
Добавлено: 10 октября 2017
Статья
Kalinin N. Journal of Knot Theory and Its Ramifications. 2015. Vol. 24. No. 12. P. 1-22.
Добавлено: 10 октября 2017
Статья
Markaryan N. S. Journal of Knot Theory and Its Ramifications. 2016. Vol. 26. No. 12.

Given a Lie algebra with a scalar product, one may consider the latter as a symplectic structure on a $dg$-scheme, which is the spectrum of the Chevalley--Eilenberg algebra. In the first section we explicitly calculate the first order deformation of the differential on the Hochschild complex of the Chevalley--Eilenberg algebra. The answer contains the Duflo character. This calculation is used in the last section. There we sketch the definition of the Wilson loop invariant of knots, which is, hopefully, equal to the Kontsevich integral, and show that for unknot they coincide. As a byproduct, we get a new proof of the Duflo isomorphism for a Lie algebra with a scalar product.

Добавлено: 10 февраля 2016