Density of isoperimetric spectra

Abstract

We show that the set of $k$–dimensional isoperimetric exponents of finitely presented groups is dense in the interval $\left\{t\in ℝ|t\ge 1\right\}$ for $k\ge 2$. Hence there is no higher-dimensional analogue of Gromov’s gap $\left(1,2\right)$ in the isoperimetric spectrum.