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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The automorphism group of a free group is not a $ {\rm CAT}(0)$ group


Author: S. M. Gersten
Journal: Proc. Amer. Math. Soc. 121 (1994), 999-1002
MSC: Primary 20F32; Secondary 20E05, 20F28, 53C23, 57M07
MathSciNet review: 1195719
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Abstract: If F is a finitely generated free group, then the group $ {\operatorname{Aut}}(F)$, if $ {\text{rank}}(F) \geq 3$, and $ {\text{Out}}(F)$, if $ {\text{rank}}(F) \geq 4$, are not isomorphic to a subgroup of a group which acts properly discontinuously and cocompactly on a 1-connected geodesic metric space satisfying Gromov's condition $ {\text{CAT}}(0)$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1195719-9
PII: S 0002-9939(1994)1195719-9
Keywords: Free group, automorphism, $ {\text{CAT}}(0)$, geodesic metric space
Article copyright: © Copyright 1994 American Mathematical Society