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G&T Monographs |
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Density of isoperimetric spectra
Noel Brady and Max Forester
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Geometry & Topology 14 (2010)
435–472
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Abstract
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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.
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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
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Mathematical Subject Classification
Primary: 20F65
Secondary: 20E06, 20F69, 53C99, 57M07
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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
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