New York Journal of Mathematics
Volume 8 (2002) 169-179


José Burillo and Jennifer Taback

Equivalence of Geometric and Combinatorial Dehn Functions

Published: November 6, 2002
Keywords: Dehn function, van Kampen diagram
Subject: Primary 20F65; secondary: 20F05, 20F06, 49Q15

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.

Author information

José Burillo:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
Current Address: Universitat Politecnica de Catalunya, Castelldefels (Barcelona), Spain

Jennifer Taback:
Dept. of Mathematics and Statistics, University at Albany, Albany, NY 12222