Structural stability of Kleinian groups.

Classification of Kleinian Groups

We present here a complete classification of those Kleinian groups which have an invariant region of discontinuity and which, in their action on hyperbolic 3-space, have a finite-sided fundamental polyhedron. This classification is complete in the same sense that finitely-generated Fuchsian groups of the first kind are completely classified, i.e., there is a countable collection of topologicall...

Computing arithmetic Kleinian groups

Arithmetic Kleinian groups are arithmetic lattices in PSL2(C). We present an algorithm that, given such a group Γ, returns a fundamental domain and a finite presentation for Γ with a computable isomorphism.

Divergent sequences of Kleinian groups

One of the basic problems in studying topological structures of deformation spaces for Kleinian groups is to find a criterion to distinguish convergent sequences from divergent sequences. In this paper, we shall give a sufficient condition for sequences of Kleinian groups isomorphic to surface groups to diverge in the deformation spaces. AMS Classification 57M50; 30F40

Commensurability riteria for Kleinian groups

Kleinian Groups and Holomorphic Dynamics

In this work we explore some relations between iteration theory and theory of Kleinian groups. There is already work done in that direction. In the case of Fuchsian groups there is the result of Bowen and Series [1979] which guarantees the existence of a boundary map, orbit equivalent to the action of the Fuchsian group on the hyperbolic plane. We use this result in Sec. 3. Brooks and Matelski ...