Volume 13, issue 2 (2009)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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 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 2000
Primary: 20F36, 20F28
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