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

Day, Matthew B¹

¹ Department of Mathematics, California Institute of Technology, 1200 E California Blvd, Pasadena, CA 91101, USA

Geometry & topology, Tome 13 (2009) no. 2, pp. 817-855.

Résumé

We generalize the peak reduction algorithm (Whitehead’s theorem) for free groups to a theorem about a general right-angled Artin group $A_{\Gamma }$. As an application, we find a finite presentation for the automorphism group $Aut{A}_{\Gamma }$ 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.

Détail

DOI : 10.2140/gt.2009.13.817

Keywords: peak reduction, right-angled Artin group, finite presentation

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