Homomorphisms of finitely generated Kleinian groups

The limit set intersection theorem for finitely generated Kleinian groups

The proof of the Theorem proceeds by showing that it holds in some special cases involving Kleinian groups with connected limit sets, and then extending to the general case by using a decomposition argument based on the Klein-Maskit combination theorems and a careful tracking of the limit points resulting from this decomposition. We discuss various well-behaved classes of limit points in Sectio...

Finitely Generated Abelian Groups

Finitely Generated Semiautomatic Groups

The present work shows that Cayley automatic groups are semiautomatic and exhibits some further constructions of semiautomatic groups and in particular shows that every finitely generated group of nilpotency class 3 is semiautomatic.

All finitely presentable groups from link complements and Kleinian groups

Klein defined geometry in terms of invariance under groups actions; here we give a discrete (partial) converse of this, interpreting all (finitely presentable) groups in terms of the geometry of hyperbolic 3-manifolds (whose fundamental groups are, appropriately, Kleinian groups). For G∗ a Kleinian group of isometries of hyperbolic 3-space H, with MG∗ ∼= H3/G∗ a non-compact N -cusped orientable...

Combinatorics of Finitely Generated Groups

of the Dissertation Combinatorics of Finitely Generated Groups