|
Organizers |
Quasiconvexity in nonpositively curved spaces with isolated flats
by
G. Christopher Hruska
Cornell University
Let G act properly and cocompactly by isometries on a CAT(0) space X. A subgroup H is quasiconvex with respect to this action if an orbit Hx in X is quasiconvex. One problem with this notion is that, in general, the quasiconvexity of a subgroup depends on the choice of CAT(0) action.
A CAT(0) 2-complex has isolated flats if its flat planes stay away from each other in a certain precise sense. These complexes with isolated flats share many properties with Gromov's hyperbolic spaces which are not shared by general CAT(0) spaces.
We show that if G acts on a CAT(0) 2-complex with isolated flats, then quasiconvexity is well-defined in the following sense:
Theorem: Suppose G acts properly and cocompactly on two different CAT(0) 2-complexes X and Y, each with isolated flats. Then a subgroup H < G is quasiconvex relative to the first action if and only if it is quasiconvex relative to the second action.
Date received: September 27, 2000
Copyright © 2000 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 # cafm-09.