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hyperbolic group

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  • Hyperbolic group — In group theory, a hyperbolic group, also known as a word hyperbolic group, Gromov hyperbolic group, negatively curved group is a finitely generated group equipped with a word metric satisfying certain properties characteristic of hyperbolic… …   Wikipedia

  • Group (mathematics) — This article covers basic notions. For advanced topics, see Group theory. The possible manipulations of this Rubik s Cube form a group. In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines …   Wikipedia

  • Group theory — is a mathematical discipline, the part of abstract algebra that studies the algebraic structures known as groups. The development of group theory sprang from three main sources: number theory, theory of algebraic equations, and geometry. The… …   Wikipedia

  • Hyperbolic space — In mathematics, hyperbolic n space, denoted H n , is the maximally symmetric, simply connected, n dimensional Riemannian manifold with constant sectional curvature −1. Hyperbolic space is the principal example of a space exhibiting hyperbolic… …   Wikipedia

  • Hyperbolic geometry — Lines through a given point P and asymptotic to line R. A triangle immersed in a saddle shape plane (a hyperbolic paraboloid), as well as two diverging ultraparall …   Wikipedia

  • Hyperbolic function — A ray through the origin intercepts the hyperbola in the point , where is twice the area between the ray and the …   Wikipedia

  • Hyperbolic 3-manifold — A hyperbolic 3 manifold is a 3 manifold equipped with a complete Riemannian metric of constant sectional curvature 1. In other words, it is the quotient of three dimensional hyperbolic space by a subgroup of hyperbolic isometries acting freely… …   Wikipedia

  • Hyperbolic quaternion — In mathematics, a hyperbolic quaternion is a mathematical concept first suggested by Alexander MacFarlane in 1891 in a speech to the American Association for the Advancement of Science. The idea was criticized for its failure to conform to… …   Wikipedia

  • Hyperbolic motion — In geometry, a hyperbolic motion is a mapping of a model of hyperbolic geometry that preserves the distance measure in the model. Such a mapping is analogous to congruences of Euclidean geometry which are compositions of rotations and… …   Wikipedia

  • Hyperbolic triangle — In mathematics, the term hyperbolic triangle has more than one meaning.In the foundations of the hyperbolic functions sinh, cosh and tanh, a hyperbolic triangle is a right triangle in the first quadrant of the Cartesian plane :{(x,y):x,y in… …   Wikipedia

  • Hyperbolic Dehn surgery — In mathematics, hyperbolic Dehn surgery is an operation by which one can obtain further hyperbolic 3 manifolds from a given cusped hyperbolic 3 manifold. Hyperbolic Dehn surgery exists only in dimension three and is one which distinguishes… …   Wikipedia

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