The automorphism group of the free group of rank two is a CAT(0) group
classification
🧮 math.GR
keywords
groupautomorphismrankactscomplexfaithfullyfreegeometrically
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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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