Volume 13, issue 2 (2009)

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

Matthew B Day

Geometry & Topology 13 (2009) 817–855
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.

Keywords
peak reduction, right-angled Artin group, finite presentation
Mathematical Subject Classification 2000
Primary: 20F36, 20F28
Secondary: 20F05