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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Additional Information
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