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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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


Author: S. M. Gersten
Journal: Proc. Amer. Math. Soc. 121 (1994), 999-1002
MSC: Primary 20F32; Secondary 20E05, 20F28, 53C23, 57M07
DOI: https://doi.org/10.1090/S0002-9939-1994-1195719-9
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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Keywords: Free group, automorphism, <!– MATH ${\text {CAT}}(0)$ –> <IMG WIDTH="73" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${\text {CAT}}(0)$">, geodesic metric space
Article copyright: © Copyright 1994 American Mathematical Society