Kleinian groups with discrete length spectrum

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.

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...

Surface Subgroups of Kleinian Groups with Torsion

A subgroup of a group is known as a surface subgroup if it is isomorphic to the fundamental group of a closed connected orientable surface with positive genus. The surface subgroup conjecture in low-dimensional topology proposes that if the fundamental group of a closed orientable irreducible 3-manifold is infinite, then it contains a surface subgroup. With the recent solution to the geometrisa...

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 ...