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POLYNOMIAL DEHN FUNCTIONS AND THE LENGTH OF ASYNCHRONOUSLY AUTOMATIC STRUCTURES

Published online by Cambridge University Press:  02 August 2002

MARTIN R. BRIDSON
MARTIN R. BRIDSON
Affiliation:
Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB. bridson@maths.ox.ac.uk. Present address: Department of Mathematics, Imperial College, 180 Queen's Gate, London SW7 2BZ
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Abstract

We extend the range of observed behaviour among length functions of optimal asynchronously automatic structures. We do so by means of a construction that yields asynchronously automatic groups with finite aspherical presentations where the Dehn function of the group is polynomial of arbitrary degree. Many of these groups can be embedded in the automorphism group of a free group. Moreover, the fact that the groups have aspherical presentations makes them useful tools in the search to determine the spectrum of exponents for second order Dehn functions. We contribute to this search by giving the first exact calculations of groups with quadratic and superquadratic exponents.

2000 Mathematical Subject Classification:20F06, 20F65, 20F69.

Keywords

isoperimetric functionsfinitely presented groupsgrowth of automorphismsautomatic structures
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 85 , Issue 2 , September 2002 , pp. 441 - 466
Copyright
2002 London Mathematical Society

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