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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Fractional isoperimetric inequalities
and subgroup distortion


Author: Martin R. Bridson
Journal: J. Amer. Math. Soc. 12 (1999), 1103-1118
MSC (1991): Primary 20F32, 20F10, 20F05
Published electronically: June 9, 1999
MathSciNet review: 1678924
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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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Additional Information

Martin R. Bridson
Affiliation: Mathematical Institute, 24–29 St. Giles’, Oxford OX1 3LB, Great Britain
Email: bridson@maths.ox.ac.uk

DOI: http://dx.doi.org/10.1090/S0894-0347-99-00308-2
PII: S 0894-0347(99)00308-2
Keywords: Dehn function, isoperimetric inequality, subgroup distortion
Received by editor(s): December 23, 1996
Received by editor(s) in revised form: March 29, 1999
Published electronically: June 9, 1999
Additional Notes: This work was supported in part by NSF grant DMS-9401362 and an EPSRC Advanced Fellowship.
Dedicated: For John Stallings on his 60th birthday
Article copyright: © Copyright 1999 American Mathematical Society