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 $\textrm {CAT}(0)$ group
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by S. M. Gersten PDF

Proc. Amer. Math. Soc. 121 (1994), 999-1002 Request permission

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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