The purpose of this book is to describe the global properties of complete simply connected
spaces that are non-positively curved in the sense of AD Alexandrov and to examine the …

THERE IS ONLY ONE GAP IN THE ISOPERIMETRIC SPECTRUM N. Brady and MR Bridson
Page 1 GAFA, Geom. funct. anal. Vol. 10 (2000) 1053 – 1070 1016-443X/00/0501053-18 …

If the finitely presented group G splits over the finitely presented sub-group C, then classes
are constructed in H 2 (∞)(G) which reflect the splitting and which serve as lower bounds for …

The isoperimetric profile of a finitely generated group Γ is an asymptotic invariant which can
be used to measure the degree of amenability of Γ. Another measure of the degree of …

In this paper we generalize the setting and results of [1] to higher dimensions. The main
results are Theorem 2 (invariance of Dehn functions under quasi-retractions in the sense of …

The k–dimensional Dehn (or isoperimetric) function of a group bounds the volume of
efficient ball-fillings of k–spheres mapped into k–connected spaces on which the group acts …

Homological and homotopical higher-order filling functions Page 1 Groups Geom. Dyn. 5 (2011),
683–690 DOI 10.4171/GGD/144 Groups, Geometry, and Dynamics © European Mathematical …

First order Dehn functions of groups (and to a lesser extent monoids) have been the subject
of a considerable amount of study over the last decade. Let us review the definition of these …

The geometry of group extensions Page 1 J. Group Theory 1 (1998) 395±416 Journal of
Group Theory ( de Gruyter 1998 The geometry of group extensions YG Baik, J. Harlander and …

We introduce the notion of an R-combing and use it to show that hyperbolic groups satisfy
linear isoperimetric inequalities for filling real cycles in each positive dimension. S. Gersten …