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arXiv · 0809.2034

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

Adam Piggott·Kim Ruane·Genevieve S. Walsh
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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.

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Adam Piggott, Kim Ruane, Genevieve S. Walsh. 2008-09-11. The automorphism group of the free group of rank two is a CAT(0) group. https://doi.org/10.1307/mmj/1281531457

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