### There is only one gap in the isoperimetric spectrum

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