Quasi-actions on trees
by
Lee Mosher
Rutgers University, Newark
Coauthors: Kevin Whyte (Univ. of Utah)

Suppose Gamma is a graph of finitely generated groups with fundamental group G. A quasi-isometric geometer wants to know: If H is a finitely generated group quasi-isometric to G, is H the fundamental group of a graph of groups, with vertex and edge groups quasi-isometric to those in Gamma? I'll talk about some techniques to approach this question, developed in recent joint work with Kevin Whyte. Some of the theorems we can prove with these techniques are: (1) If H is quasi-isometric to an accessible group (that is, the fundamental group of a graph of one-ended and finite vertex groups with finite edge groups), then H is accessible. (2) If H is quasi-isometric to a graph of virtually cyclic groups, (or virtually abelian groups, or virtually nilpotent groups, or finite-by-Fuchsian groups, or...) then H is a graph of groups of the same type. In this theorem, the vertex groups and the edge groups all belong to the same qi-class, and the edge-to-vertex injections are all of finite index.

Date received: May 14, 1999

Copyright © 1999 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 # cada-05.