Peak reduction and finite presentations for automorphism groups of right-angled Artin groups

Details Peak reduction and finite presentations for automorphism groups of right-angled Artin groups Peak reduction and finite presentations for automorphism groups of right-angled Artin groups

2008-07-30

arxiv.org/abs/0807.4799v1

Mathematics

Group Theory

41 pages

Scientific paper

We generalize the peak-reduction algorithm (Whitehead's theorem) for free groups to a theorem about a general right-angled Artin group A_Gamma. As an application, we find a finite presentation for the automorphism group Aut A_Gamma that generalizes McCool's presentation for the automorphism group of a finite rank free group. We also give consider a stronger generalization of peak-reduction, giving a counterexample and proving a special case.

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