Geometric convergence actions
by
Victor Gerasimov
University of Minas Gerais, Brasil. & Institute of Mathematics, Novosibirsk, Russia

We study a class of convergence actions of finitely generated groups that contains the geometrically finite actions, the actions of finitely generated groups on its Floyd boundaries, the convergence actions on totally disconnected spaces and others. We call actions in this class geometric. Some known theorems and conjectures claim that certain actions are geometric. No example of non-geometric convergence action is known. On the other hand geometric actions have properties that are not evident for arbitrary convergence action. For any finitely generated group it is defined the universal geometric action. It coincides with the action on the boundary in the case of hyperbolic group. The connected components of the space of the universal action are the ends of the group. Every minimal geometric action is uniquely a quotient of the universal.

Date received: October 20, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajt-10.