Geometry & Topology Volume 14, issue 1 (2010)

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).

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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