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pro vyhledávání: '"Manturov, V."'
Autor:
Manturov, V. O., Nikonov, I. M.
The motivation for this work is to construct a map from classical knots to virtual ones. What we get in the paper is a series of maps from knots in the full torus (thickened torus) to flat-virtual knots. We give definition of flat-virtual knots and p
Externí odkaz:
http://arxiv.org/abs/2406.12864
In the present paper we develop the techniques suggested in \cite{ManturovNikonov} and the photography principle \cite{ManturovWan} for constructing an invariant of 3-manifolds based on Ptolemy relation. We show that a direct implementation of the te
Externí odkaz:
http://arxiv.org/abs/2307.03437
Autor:
Manturov, V. O., Nikonov, I. M.
Using the recoupling theory, we define a representation of the pure braid group and show that it is not trivial.
Comment: 4 pages
Comment: 4 pages
Externí odkaz:
http://arxiv.org/abs/2303.04423
Autor:
Manturov, V. O., Nikonov, I. M.
In the present paper, we address the problem how to get a map from knots in the cylinder and on the thickened torus to some (generalisation of) virtual knots called virtual-flat knots. The main construction takes a diagram on a cylinder (torus) and a
Externí odkaz:
http://arxiv.org/abs/2210.09689
Autor:
Manturov, V. O., Nikonov, I. M.
Virtual knot theory has experienced a lot of nice features that did not appear in classical knot theory, e.g., parity and picture-valued invariants. In the present paper we use virtual knot theory effects to construct new representations of classical
Externí odkaz:
http://arxiv.org/abs/2210.06862
The spaces of triangulations of a given manifold have been widely studied. The celebrated theorem of Pachner~\cite{Pachner} says that any two triangulations of a given manifold can be connected by a sequence of bistellar moves, or Pachner moves, see
Externí odkaz:
http://arxiv.org/abs/1912.02695
Autor:
Akimova, A. A., Manturov, V. O.
In the present paper, we develop a picture formalism which gives rise to an invariant that dominates several known invariants of classical and virtual knots: the Jones polynomial, the Kuperberg bracket, and the normalised arrow polynomial.
Externí odkaz:
http://arxiv.org/abs/1907.06502
Autor:
Manturov, V. O., Kim, S.
We construct a group $\Gamma_{n}^{4}$ corresponding to the motion of points in $\mathbb{R}^{3}$ from the point of view of Delaunay triangulations. We study homomorphisms from pure braids on $n$ strands to the product of copies of $\Gamma_{n}^{4}$. We
Externí odkaz:
http://arxiv.org/abs/1902.11238
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