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.Comment: 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 correcte
