Results 11 to 20 of about 189,122 (232)
Acylindrically hyperbolic groups [PDF]
Transactions of the American Mathematical Society, 2015 We say that a group G G is acylindrically hyperbolic if it admits a non-elementary acylindrical action on a hyperbolic space. We prove that the class of acylindrically hyperbolic groups coincides with many other classes studied in the literature, e.g., the class C g e o m
Osin, D.
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An Extension of Poincare Model of Hyperbolic Geometry with Gyrovector Space Approach [PDF]
Mathematics Interdisciplinary Research, 2016 The aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. In [1], Ungar and Chen showed that the algebra of the group SL(2, C) naturally leads to the notion of gyrogroups and gyrovector spaces for dealing ...
Mahfouz Rostamzadeh +1 more
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Axioms, 2023 Hyperbolic triangle groups are found within the category of finitely generated groups. These are topological groups formed by the reflections along the sides of a hyperbolic triangle and acting properly discontinuously on the hyperbolic plane.
Sajida Younas +3 more
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Amenable hyperbolic groups [PDF]
Journal of the European Mathematical Society, 2015 We give a complete characterization of the locally compact groups that are non elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting automorphisms. We moreover give a description of all Gromov-hyperbolic locally compact groups with a cocompact amenable ...
Pierre-Emmanuel Caprace +3 more
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Lacunary hyperbolic groups [PDF]
Geometry & Topology, 2009 69 pages; v2: added an Appendix by M. Kapovich and B.
Ol’shanskii, Alexander Yu +2 more
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Statistical hyperbolicity of relatively hyperbolic groups [PDF]
Algebraic & Geometric Topology, 2016 12 pages; Several corrections and improvements on the exposition after referee report.
Osborne, Jeremy, Yang, Wen-yuan
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Relative hyperbolicity of hyperbolic-by-cyclic groups
Groups, Geometry, and Dynamics, 2023 Let G be a torsion-free hyperbolic group and \alpha an automorphism of G . We show that there exists a canonical collection of subgroups that are polynomially growing under
Dahmani, François, Krishna M S, Suraj
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Quasi-hyperbolic planes in hyperbolic groups [PDF]
Proceedings of the American Mathematical Society, 2005 The hyperbolic plane admits a quasi-isometric embedding into a hyperbolic group if and only if the group is not virtually free.
Bruce Kleiner, Mario Bonk
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AIMS Mathematics, 2023 The idea of sine hyperbolic fractional orthotriple linear Diophantine fuzzy sets (sinh-FOLDFSs), which allows more uncertainty than fractional orthotriple fuzzy sets (FOFSs) is noteworthy.
Muhammad Naeem +3 more
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Hyperbolic structures on groups [PDF]
Algebraic & Geometric Topology, 2019 For every group $G$, we introduce the set of hyperbolic structures on $G$, denoted $\mathcal{H}(G)$, which consists of equivalence classes of (possibly infinite) generating sets of $G$ such that the corresponding Cayley graph is hyperbolic; two generating sets of $G$ are equivalent if the corresponding word metrics on $G$ are bi-Lipschitz equivalent ...
Abbott, Carolyn +2 more
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