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arXiv · 1306.6549

On the number of outer automorphisms of the automorphism group of a right-angled Artin group

Neil J. Fullarton
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Abstract

We show that there is no uniform upper bound on |Out(Aut(A))| when A ranges over all right-angled Artin groups. This is in contrast with the cases where A is free or free abelian: for all n, Dyer-Formanek and Bridson-Vogtmann showed that Out(Aut(F_n)) = 1, while Hua-Reiner showed |Out(Aut(Z^n)| = |Out(GL(n,Z))| < 5. We also prove the analogous theorem for Out(Out(A)). We establish our results by giving explicit examples; one useful tool is a new class of graphs called austere graphs.

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Neil J. Fullarton. 2013-06-27. On the number of outer automorphisms of the automorphism group of a right-angled Artin group. https://arxiv.org/abs/1306.6549

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