Density of isoperimetric spectra

Brady, Noel¹ ; Forester, Max¹

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

Geometry & topology, Tome 14 (2010) no. 1, pp. 435-472.

Résumé

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.

Détail

DOI : 10.2140/gt.2010.14.435

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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