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G&T Monographs |
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Peak reduction and finite presentations for automorphism
groups of right-angled Artin groups
Matthew B Day
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Geometry & Topology 13 (2009)
817–855
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Abstract
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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.
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Keywords
peak reduction, right-angled Artin group,
finite presentation
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Mathematical Subject Classification
Primary: 20F28, 20F36
Secondary: 20F05
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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
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