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

Abstract

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 consider a stronger generalization of peak reduction, giving a counterexample and proving a special case.