Fractional isoperimetric inequalities and subgroup distortion

Bridson, Martin

doi:10.1090/S0894-0347-99-00308-2

Fractional isoperimetric inequalities and subgroup distortion
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by Martin R. Bridson

J. Amer. Math. Soc. 12 (1999), 1103-1118

DOI: https://doi.org/10.1090/S0894-0347-99-00308-2

Published electronically: June 9, 1999

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Abstract:

It is shown that there exist infinitely many non-integers $r>2$ such that the Dehn function of some finitely presented group is $\simeq n^r$. Explicit examples of such groups are constructed. For each rational number $s\ge 1$ pairs of finitely presented groups $H\subset G$ are constructed so that the distortion of $H$ in $G$ is $\simeq n^s$.

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