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There is only one gap in the isoperimetric spectrum

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Abstract.

The closure of the set of isoperimetric exponents for finitely presented groups is \( \{1\} \cup [2,\infty \). For each pair of positive integers \( p \ge q \), one can construct groups with aspherical presentations for which the Dehn function is \( \simeq n^{2\alpha} \), where \( \alpha\,={\rm log}_{2}(2p/q) \).

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Authors and Affiliations

  1. Department of Mathematics, University of Oklahoma, 73019, Norman, OK, USA

    N. Brady

  2. Mathematical Institute, 24—29 St Giles', OX1 3LB, Oxford, UK

    M.R. Bridson

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  1. N. Brady
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  2. M.R. Bridson
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Correspondence to N. Brady.

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Submitted: April 1999, Revised version: April 2000.

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Brady, N., Bridson, M. There is only one gap in the isoperimetric spectrum . GAFA, Geom. funct. anal. 10, 1053–1070 (2000). https://doi.org/10.1007/PL00001646

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  • DOI: https://doi.org/10.1007/PL00001646

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