WebMar 24, 2024 · A discrete group is a topological group with the discrete topology. Often in practice, discrete groups arise as discrete subgroups of continuous Lie groups acting on a geometric space. For example, SL_2(Z) is a discrete group, realized as a subgroup of the special linear group SL_2(R) acting on the upper half-plane by Möbius … WebThis text is intended to serve as an introduction to the geometry of the action of discrete groups of Mobius transformations. The subject matter has now been studied with changing points of emphasis for over a …

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WebThis text is intended to serve as an introduction to the geometry of the action of discrete groups of Mobius transformations. The subject matter has now been studied with changing points of emphasis for over a hundred years, the most recent developments being connected with the theory of 3-manifolds: see, for example, the papers of Poincare [77] … WebSep 6, 2024 · This group has a Teichmuller space, which is the space of (suitably … shop saber router bits

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WebIn mathematics, groups naturally arise as symmetries of geometric ob-jects. The … WebMar 15, 2024 · Fuchsian group. A discrete group of holomorphic transformations (cf. Discrete group of transformations) of an (open) disc $ K $ onto the Riemann sphere, that is, of a disc or a half-plane onto the complex plane. Most often one takes for $ K $ the upper half-plane. $$ U = \ { {z \in \mathbf C } : { \mathop {\rm Im} z > 0 } \} $$. or the unit disc. WebMar 24, 2024 · A group G is a finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of closure, associativity, the identity property, … shops 96 st john indiana