Equivalence of geometric and combinatorial Dehn functions

Abstract:

We prove that if a finitely presented group acts properly discontinuously, cocompactly and by isometries on a simply connected Riemannian manifold, then the Dehn function of the group and the corresponding filling function of the manifold are equivalent, in a sense described below. We also prove this result for simplicial complexes $X$ where the metric on $X$ restricts to a Riemannian metric with corners on each simplex.

José Burillo :
Departament de Matemátiques, Universitat Autónoma de Barcelona, 08193 Bellaterra, Spain
Current Address: Universitat Politecnica de Catalunya, Castelldefels (Barcelona), Spain
burillo@mat.upc.es

Jennifer Taback:
Dept. of Mathematics and Statistics, University at Albany, Albany, NY 12222
jtaback@math.albany.edu
http://math.albany.edu:8000/~jtaback