The automorphism group of a free group is not a 𝐶𝐴𝑇(0) group

Gersten, S. M.

doi:10.1090/S0002-9939-1994-1195719-9

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
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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