Monodromy Groups

1. All of the discrete groups involved are explicitly presentable as monodromy groups, and most (but not all) are arithmetic.

Hyperbolic Geometry

1. The first part is concerned with hyperbolic geometry and discrete groups.

Topological Groups

1. By replacing the discrete groups with topological groups, you get the more general notion of a principle fiber bundle.

Complex Group

1. Note that for discrete groups, C c(G) is the same thing as the complex group ring C G.

Examples

1. There are also examples of discrete groups generated by reflections on the other simply connected space of constant curvature, hyperbolic n -space, [H.sup. (Web site)

Groups

1. Hence, there is an isomorphism between the category of groups and the category of discrete groups. (Web site)

Covering Spaces

1. In geometric group theory, post- Gromov, discrete groups have been studied in terms of the local curvature properties of orbihedra and their covering spaces. (Web site)

Isometries

1. Discrete groups of isometries of hyperbolic space. (Web site)
2. There is a similar theory of discrete groups of isometries generated by affine reflections on Euclidean space [E.sup. (Web site)

Compact Groups

1. In fact, the only abelian categories of topological abelian groups I am aware of are the discrete groups and the dual category of compact groups.

Finite Groups

1. Moreover, discrete groups correspond to compact abelian groups; finite groups correspond to finite groups.

Discrete Symmetries

1. Discrete symmetries are described by discrete groups.

Algebraists

1. Indeed, analysts may refer to the ordinary, non-topological groups studied by algebraists as " discrete groups ".

Discrete Groups

1. Examples Every group can be trivially made into a topological group by considering it with the discrete topology; such groups are called discrete groups. (Web site)
2. Examples of unimodular groups are abelian groups, compact groups, discrete groups, semisimple Lie groups and connected nilpotent Lie groups. (Web site)

Categories

1. Compact Groups
2. Algebraists
3. Topological Group
4. Discrete Symmetries
5. Semisimple Lie Groups
6. Books about "Discrete Groups" in Amazon.com
   

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