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On the Geometry of the Automorphism Group of a Free Group

On the Geometry of the Automorphism Group of a Free Group The groups Aut(F3) and Out(F3) satisfy strictly exponential isoperimetric inequalities; in particular, they are not automatic. For n ⩾ 3, Aut (Fn) and Out (Fn) do not admit bounded bicombings of sub‐exponential length, hence they cannot act properly and cocompactly by isometries on any simply‐connected space of non‐positive curvature, and they are not biautomatic. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

On the Geometry of the Automorphism Group of a Free Group

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Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/27.6.544
Publisher site
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Abstract

The groups Aut(F3) and Out(F3) satisfy strictly exponential isoperimetric inequalities; in particular, they are not automatic. For n ⩾ 3, Aut (Fn) and Out (Fn) do not admit bounded bicombings of sub‐exponential length, hence they cannot act properly and cocompactly by isometries on any simply‐connected space of non‐positive curvature, and they are not biautomatic.

Journal

Bulletin of the London Mathematical Society – Wiley

Published: Nov 1, 1995

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