Geometry & Topology

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

Matthew B Day

Full-text: Open access

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.

Article information

Source
Geom. Topol., Volume 13, Number 2 (2009), 817-855.

Dates
Received: 31 July 2008
Revised: 4 December 2008
Accepted: 22 November 2008
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800218

Digital Object Identifier
doi:10.2140/gt.2009.13.817

Mathematical Reviews number (MathSciNet)
MR2470964

Zentralblatt MATH identifier
1226.20024

Subjects
Primary: 20F36: Braid groups; Artin groups 20F28: Automorphism groups of groups [See also 20E36]
Secondary: 20F05: Generators, relations, and presentations

Keywords
peak reduction right-angled Artin group finite presentation

Citation

Day, Matthew B. Peak reduction and finite presentations for automorphism groups of right-angled Artin groups. Geom. Topol. 13 (2009), no. 2, 817--855. doi:10.2140/gt.2009.13.817. https://projecteuclid.org/euclid.gt/1513800218


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References

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