COHOMOLOGY 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.

Digital cohomology groups of certain minimal surfaces

In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups of minimal simple surfaces. We also prove some theorems related to degree properties of a map on digital sph...

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