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Geometrically Finite Kleinian Groups
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Abstract
Kleinian groups which are cofinite (namely, which correspond to complete hyperbolic 3-manifolds with finite volume) have several desirable properties. The cofiniteness can be generalized to the concept of geometric finiteness, which we discuss in this chapter. In Section 3.1, we give various definitions of geometrically finite Kleinian groups and prove that they are equivalent. Next in Section 3.2 we explain some of the fundamental properties of such groups. In Section 3.3, we consider the variety and rigidity of geometrically finite hyperbolic structures admitted in a given topological manifold or represented by isomorphic Kleinian groups.
Oxford University PressOxford
Title: Geometrically Finite Kleinian Groups
Description:
Abstract
Kleinian groups which are cofinite (namely, which correspond to complete hyperbolic 3-manifolds with finite volume) have several desirable properties.
The cofiniteness can be generalized to the concept of geometric finiteness, which we discuss in this chapter.
In Section 3.
1, we give various definitions of geometrically finite Kleinian groups and prove that they are equivalent.
Next in Section 3.
2 we explain some of the fundamental properties of such groups.
In Section 3.
3, we consider the variety and rigidity of geometrically finite hyperbolic structures admitted in a given topological manifold or represented by isomorphic Kleinian groups.
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