Related papers: On the potential functions for the hyperbolic stru…

Recently, there has been a rising surge of momentum for deep representation learning in hyperbolic spaces due to theirhigh capacity of modeling data like knowledge graphs or synonym hierarchies, possessing hierarchical structure. We refer…

This paper exhibits an infinite family of hyperbolic knot complements that have three knot complements in their respective commensurability classes.

This work deals with function theory on quantum complex hyperbolic spaces. The principal notions are expounded. We obtain explicit formulas for invariant integrals on `finite' functions on a quantum hyperbolic space and on the associated…

We construct a Cantor set in S^3 whose complement admits a complete hyperbolic metric.

We provide a diagrammatic criterion for semi-adequate links to be hyperbolic. We also give a conjectural description of the satellite structures of semi-adequate links. One application of our result is that the closures of sufficiently…

We define and study "hyperbolic forcing".

In this work we introduce a mapping between the so called deformed hyperbolic potentials, which are presenting a continuous interest in the last few years, and the corresponding nondeformed ones. As a consequence, we conclude that these…

A construction of a spatial graph from a strongly invertible knot was developed by the second author, and a necessary and sufficient condition for the given spatial graph to be hyperbolic was provided as well. The condition is improved in…

This book is an introduction to hyperbolic geometry in dimension three, and its applications to knot theory and to geometric problems arising in knot theory. It has three parts. The first part covers basic tools in hyperbolic geometry and…

In this article we give evaluations of certain series of hyperbolic functions, using Jacobi elliptic functions theory. We also define some new functions that enable us to give characterization of not solvable class of series.

We define and study an extended hyperbolic space which contains the hyperbolic space and de Sitter space as subspaces and which is obtained as an analytic continuation of the hyperbolic space. The construction of the extended space gives…

We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.

We define and study hyperbolic extensions.

In this article we give evaluations of certain series of hyperbolic functions using Jacobi elliptic functions theory. We also define some new functions that enable us to give characterization of not solvable class of series.

A system of commutative hyperbolic complex numbers in 2 dimensions is studied in this paper. Exponential and trigonometric forms are obtained for these hyperbolic twocomplex numbers. Expressions are given for the elementary functions of…

We investigate the geometry of hyperbolic knots and links whose diagrams have a high amount of twisting of multiple strands. We find information on volume and certain isotopy classes of geodesics for the complements of these links, based…

Crochet models of a hyperbolic plane is a popular educational tool as they help to visualize complicated objets in hyperbolic geometry. We present another way how to make crochet models when we view them as a part of a triangulated…

We present a construction of sequences of closed hyperbolic surfaces that have long systoles which form pants decompositions of these surfaces. The length of the systoles of these surfaces grows logarithmically as a function of their genus.

A knot complement admits a pseudo-hyperbolic structure by solving Thurston's gluing equations for an octahedral decomposition. It is known that a solution to these equations can be described in terms of region variables, also called…

We derive bounds on the length of the meridian and the cusp volume of hyperbolic knots in terms of the topology of essential surfaces spanned by the knot. We provide an algorithmically checkable criterion that guarantees that the meridian…