We show that the set of k–dimensional isoperimetric exponents of finitely presented
groups is dense in the interval {t in R|t ≥ 1} for k ≥ 2. Hence there is no
higher-dimensional analogue of Gromov’s gap (1,2) in the isoperimetric
spectrum.
We dedicate this paper to the memory
of John Stallings (1935–2008).
Received: 24 January 2009
Accepted: 1 October 2009
Preview posted: 29 October 2009
Published: 2 January 2010
Proposed: Walter Neumann
Seconded: Martin Bridson, Colin Rourke