The automorphism group of the free group of rank two is a CAT(0) group

Abstract

We prove that the automorphism group of the braid group on four strands acts faithfully and geometrically on a CAT(0) 2-complex. This implies that the automorphism group of the free group of rank two acts faithfully and geometrically on a CAT(0) 2-complex, in contrast to the situation for rank three and above.

7 pages, 2 figures. The manuscript has been modified in minor ways in accordance with a referee's recommendations, and a misattribution of the result "Aut F_2 is biautomatic" has been corrected

References in corpus (1)

• Quasiflats in CAT(0) complexes

Cited by in corpus (4)

• Bowditch's Q-conditions and Minsky's primitive stability
• Equivariant Morse theory on Vietoris-Rips complexes & universal spaces for proper actions
• The Geometry of Outer Automorphism Groups of Universal Right-Angled Coxeter Groups
• $\mathrm{CAT}(0)$ Extensions of Right-angled Coxeter Groups