Adam Piggott, Kim Ruane, Genevieve S. Walsh
Published 2008-09-11, updated 2009-02-25Version 3
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.
Comments: 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
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