In group theory, more precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely...
21 KB (2,753 words) - 18:41, 26 January 2024
geometry Hyperbolic group, a finitely generated group equipped with a word metric satisfying certain properties characteristic of hyperbolic geometry...
3 KB (426 words) - 03:38, 18 March 2024
geometric group theory, an acylindrically hyperbolic group is a group admitting a non-elementary 'acylindrical' isometric action on some geodesic hyperbolic metric...
10 KB (1,443 words) - 16:33, 5 May 2022
relatively hyperbolic groups are the fundamental groups of complete noncompact hyperbolic manifolds of finite volume. A group G is relatively hyperbolic with...
6 KB (868 words) - 02:45, 23 June 2023
classical hyperbolic geometry and of trees. Hyperbolicity is a large-scale property, and is very useful to the study of certain infinite groups called Gromov-hyperbolic...
20 KB (3,149 words) - 09:41, 31 July 2024
In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate...
56 KB (7,019 words) - 21:44, 8 August 2024
In mathematics, a Kleinian group is a discrete subgroup of the group of orientation-preserving isometries of hyperbolic 3-space H3. The latter, identifiable...
18 KB (2,282 words) - 20:19, 14 June 2024
"Hyperbolic groups" that introduced the notion of a hyperbolic group (also known as word-hyperbolic or Gromov-hyperbolic or negatively curved group),...
38 KB (4,308 words) - 13:31, 7 April 2024
or the hyperbolic plane. Fuchsian groups are, by definition, discrete subgroups of the isometry group of the hyperbolic plane. A Fuchsian group that preserves...
7 KB (899 words) - 09:51, 4 June 2024
In mathematics, hyperbolic space of dimension n is the unique simply connected, n-dimensional Riemannian manifold of constant sectional curvature equal...
11 KB (1,538 words) - 00:57, 19 April 2024