arXiv subjects

Alexander Kolpakov

Publications and source records attributed to Alexander Kolpakov.

58 records · Page 4Linked to original sources

arXiv2012

Deformation of finite-volume hyperbolic Coxeter polyhedra, limiting growth rates and Pisot numbers

A connection between real poles of the growth functions for Coxeter groups acting on hyperbolic space of dimensions three and greater and algebraic integers is investigated. In particular, a geometric convergence of fundamental domains for cocompact hyperbolic Coxeter groups with finite-volume limiting polyhedron provides a relation between Salem numbers and Pisot numbers. Several examples conclude this work.

math.MG↗

arXiv2011

Volume formula for a $\mathbb{Z}_2$-symmetric spherical tetrahedron through its edge lengths

The present paper considers volume formulae, as well as trigonometric identities, that hold for a tetrahedron in 3-dimensional spherical space of constant sectional curvature +1. The tetrahedron possesses a certain symmetry: namely rotation through angle $π$ in the middle points of a certain pair of its skew edges.

math.MG↗

arXiv2011

Spherical structures on torus knots and links

The present paper considers two infinite families of cone-manifolds endowed with spherical metric. The singular strata is either the torus knot ${\rm t}(2n+1, 2)$ or the torus link ${\rm t}(2n, 2)$. Domains of existence for a spherical metric are found in terms of cone angles and volume formulæ are presented.

math.GT↗

arXiv2011

Addendum to "Spherical structures on torus knots and links"

The present paper is an addendum to "Spherical structures on torus knots and links", arXiv:1008.0312, and concerns more general case of torus knot and link cone-manifolds.

math.GT↗