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

By M. Day. 2008

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We generalize the peak reduction algorithm (Whitehead’s theorem) for free groups to a theorem about a general right-angled Artin group AΓ. As an application, we find a finite presentation for the automorphism group AutAΓ 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a401d5732c42c308c922a577390e8323094b2043