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There is only one gap in the isoperimetric spectrum

#### Noel Brady and
Martin R. Bridson

#### GAFA, vol 10 (2000), 1053--1070.

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 $\alpha=\log_2(2p/q)$.