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of 279
pro vyhledávání: '"Manturov, Vassily"'
In the present paper we discuss four ways of looking at rhombile tilings: stacking 3-dimensional cubes, elements of groups, and configurations of lines and points.
Externí odkaz:
http://arxiv.org/abs/2401.15345
Autor:
Manturov, Vassily Olegovich
In \cite{ManturovNikonovMay2023,ManturovWanMay2023} the author discovered a very general principle (called {\em the photography principle}) which allows one: a) To solve various equations (like pentagon equation) b) To construct invariants of manifol
Externí odkaz:
http://arxiv.org/abs/2309.01735
Autor:
Manturov, Vassily Olegovich
Similar pictures appear in various branches of mathematics. Sometimes this similarity gives rise to deep theorems. Mentioning such a similarity between hexagonal tilings, cubes in 3-space, configurations of lines and braid groups, we prove that braid
Externí odkaz:
http://arxiv.org/abs/2306.07079
In the present paper, we consider two applications of the pentagon equation. The first deals with actions of flips on edges of triangulations labelled by rational functions in some variables. The second can be formulated as a system of linear equatio
Externí odkaz:
http://arxiv.org/abs/2305.11945
We introduce a family of groups $\Gamma_n^k$ for integer parameters $n>k$. These groups originate from discussion of braid groups on $2$-surfaces. On the other hand, they turn out to be related to 3-manifolds (in particular, they lead to new relation
Externí odkaz:
http://arxiv.org/abs/2305.06316
Autor:
Manturov, Vassily Olegovich
The aim of this article is to prove that the kernel of the map from the pure braid group $PB_{n},n\ge 4$ to the group $G_{n}^{3}$ consists of full twist braids and their exponents. The proof consists of two parts. The first part which deals with $n=4
Externí odkaz:
http://arxiv.org/abs/2210.13338
Knot concordance plays a crucial role in the low dimensional topology. We propose a very elementary techniques which allows one to construct a lot of sliceness obstructions for knots in the full torus. Our approach deals with group theoretical techni
Externí odkaz:
http://arxiv.org/abs/2203.11040
Autor:
Manturov, Vassily Olegovich
We construct an invariant of virtual knots which is a sliceness obstruction and sensitive to the $\Delta$-move. This invariants works if $\Z_{2}\oplus \Z_{2}$-index of chords is present.
Comment: 8 pages, 1 Figure
Comment: 8 pages, 1 Figure
Externí odkaz:
http://arxiv.org/abs/2201.00209
It is well known that if there exists a finite set of convex bodies on the plane with non-overlapping interiors, then there is at least one "extremal" one among them, i.e., some one which can be continuously "taken away to the infinity" (outside a la
Externí odkaz:
http://arxiv.org/abs/2109.06426
We prove a new result about the mutual behavior of irrationality measure functions $\psi_{\alpha_j}(t)$ for $n$ different real numbers $\alpha_j,\, j =1,...n$.
Comment: in German, this version contains minor corrections
Comment: in German, this version contains minor corrections
Externí odkaz:
http://arxiv.org/abs/2108.08778