#### Volume 14, issue 1 (2010)

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Density of isoperimetric spectra

### Noel Brady and Max Forester

Geometry & Topology 14 (2010) 435–472
##### Abstract

We show that the set of $k$–dimensional isoperimetric exponents of finitely presented groups is dense in the interval $\left\{t\in ℝ|t\ge 1\right\}$ for $k\ge 2$. Hence there is no higher-dimensional analogue of Gromov’s gap $\left(1,2\right)$ 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 2000
Primary: 20F65
Secondary: 20F69, 20E06, 57M07, 53C99
##### 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