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Density of isoperimetric spectra

Noel Brady and Max Forester

Geometry & Topology 14 (2010) 435–472

DOI: 10.2140/gt.2010.14.435
Abstract

We show that the set of k–dimensional isoperimetric exponents of finitely presented groups is dense in the interval {t in R|t ≥ 1} for k ≥ 2. Hence there is no higher-dimensional analogue of Gromov’s gap (1,2) in the isoperimetric spectrum.

We dedicate this paper to the memory of John Stallings (1935–2008).
Keywords

Dehn function, isoperimetric inequality, filling invariant, isoperimetric spectrum, high dimensional Dehn function, abelian-by-cyclic, admissible map, transverse map, generalized handle decomposition
Mathematical Subject Classification

Primary: 20F65

Secondary: 20E06, 20F69, 53C99, 57M07
References
Publication

Received: 24 January 2009
Accepted: 1 October 2009
Preview posted: 29 October 2009
Published: 2 January 2010
Proposed: Walter Neumann
Seconded: Martin Bridson, Colin Rourke
Authors
Noel Brady
Mathematics Department
University of Oklahoma
Norman, OK 73019
USA
http://math.ou.edu/~nbrady
Max Forester
Mathematics Department
University of Oklahoma
Norman, OK 73019
USA
http://math.ou.edu/~forester