Premium
On the Geometry of the Automorphism Group of a Free Group
Author(s) -
Bridson Martin R.,
Vogtmann Karen
Publication year - 1995
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/27.6.544
Subject(s) - mathematics , outer automorphism group , alternating group , group (periodic table) , inner automorphism , automorphism , automorphism group , quaternion group , free group , geometry , so(8) , combinatorics , chemistry , organic chemistry
The groups Aut( F 3 ) and Out( F 3 ) satisfy strictly exponential isoperimetric inequalities; in particular, they are not automatic. For n ⩾ 3, Aut ( F n ) and Out ( F n ) 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.