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

Equivalence of geometric and combinatorial Dehn functions

José Burillo and Jennifer Taback

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 Matemátiques, Universitat Autónoma 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