Zobrazeno 1 - 10
of 132
pro vyhledávání: '"Vesnin, Andrei"'
Autor:
Oshmarina, Olga, Vesnin, Andrei
Let $K_n$ be a complete graph with $n$ vertices. An embedding of $K_n$ in $S^3$ is called a spatial $K_n$-graph. Knots in a spatial $K_n$-graph corresponding to simple cycles of $K_n$ are said to be constituent knots. We consider the case $n=4$. The
Externí odkaz:
http://arxiv.org/abs/2404.12264
In this paper we provide a generalized construction of nonarithmetic hyperbolic orbiifolds in the spirit of Gromov and Piatetski-Shapiro. Nonarithmeticity of such orbifolds is based on recently obtained results connecting a behaviour of the so-called
Externí odkaz:
http://arxiv.org/abs/2307.07000
Autor:
Egorov, Andrey, Vesnin, Andrei
A polyhedron in a three-dimensional hyperbolic space is said to be generalized if finite, ideal and truncated vertices are admitted. In virtue of Belletti's theorem (2021) the exact upper bound for volumes of generalized hyperbolic polyhedra with the
Externí odkaz:
http://arxiv.org/abs/2307.04543
In this paper we obtain new upper bounds on volumes of right-angled polyhedra in hyperbolic space $\mathbb{H}^3$ in three different cases: for ideal polyhedra with all vertices on the ideal hyperbolic boundary, for compact polytopes with only finite
Externí odkaz:
http://arxiv.org/abs/2111.08789
F-polynomials for virtual knots were defined by Kaur, Prabhakar and Vesnin in 2018 using flat virtual knot invariants. These polynomials naturally generalize Kauffman's affine index polynomial and use smoothing in classical crossing of a virtual knot
Externí odkaz:
http://arxiv.org/abs/2111.04526
Fullerene graphs are mathematical models of fullerene molecules. The Wiener $(r,s)$-complexity of a fullerene graph $G$ with vertex set $V(G)$ is the number of pairwise distinct values of $(r,s)$-transmission $tr_{r,s}(v)$ of its vertices $v$: $tr_{r
Externí odkaz:
http://arxiv.org/abs/2107.10105
Autor:
Egorov, Andrey, Vesnin, Andrei
We observe that fullerene graphs are one-skeletons of polyhedra, which can be realized with all dihedral angles equal to $\pi/2$ in a hyperbolic 3-dimensional space. One of the most important invariants of such a polyhedron is its volume. We are refe
Externí odkaz:
http://arxiv.org/abs/2011.02711
The main results of the paper is that we give a characteristics for an annulus sum and a once-punctured torus sum of two handlebodies to be a handlebody as follows: 1. The annulus sum $H=H_1\cup_A H_2$ of two handlebodies $H_1$ and $H_2$ is a handleb
Externí odkaz:
http://arxiv.org/abs/1908.10113
Autor:
Ivanov, Maxim, Vesnin, Andrei
Prime knots of genus one admitting diagram with at most five classical crossings were classified by Akimova and Matveev in 2014. In 2018 Kaur, Prabhakar and Vesnin introduced families of L-polynomials and F-polynomials for virtual knots which are gen
Externí odkaz:
http://arxiv.org/abs/1908.09663
Gordian complex of knots was defined by Hirasawa and Uchida as the simplicial complex whose vertices are knot isotopy classes in $\mathbb{S}^3$. Later Horiuchi and Ohyama defined Gordian complex of virtual knots using $v$-move and forbidden moves. In
Externí odkaz:
http://arxiv.org/abs/1908.05382