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Published January 8, 2009 | Published
Journal Article Open

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 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.

Additional Information

© 2009 Mathematical Sciences Publishers. Received: 31 July 2008 Revised: 4 December 2008 Accepted: 22 November 2008 Published: 8 January 2009 Proposed: Walter Neumann Seconded: Joan Birman, Leonid Polterovich. Mathematical Subject Classification Primary: 20F28, 20F36 Secondary: 20F05

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