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

Day, Matthew B

doi:10.2140/gt.2009.13.817

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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 $A_{Γ}$ . As an application, we find a finite presentation for the automorphism group $Aut A_{Γ}$ 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

Volume 13, issue 2 (2009)