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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

DOI: 10.2140/gt.2009.13.817
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.

Keywords

peak reduction, right-angled Artin group, finite presentation
Mathematical Subject Classification

Primary: 20F28, 20F36

Secondary: 20F05
References
Publication

Received: 31 July 2008
Revised: 4 December 2008
Accepted: 22 November 2008
Published: 8 January 2009
Proposed: Walter Neumann
Seconded: Joan Birman, Leonid Polterovich
Authors
Matthew B Day
Department of Mathematics
California Institute of Technology
1200 E California Blvd
Pasadena, CA 91101
USA
http://www.its.caltech.edu/~mattday