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

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

2008-09-11

arxiv.org/abs/0809.2034v3

Mathematics

Group Theory

7 pages, 2 figures. The manuscript has been modified in minor ways in accordance with a referee's recommendations, and a misat

Scientific paper

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.

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