Full-featured peak reduction in right-angled Artin groups

Day, Matthew B¹

¹Department of Mathematical Sciences, University of Arkansas, SCEN 301, Fayetteville, AR 72701, United States

Algebraic and Geometric Topology, Tome 14 (2014) no. 3, pp. 1677-1743

Résumé

We prove a new version of the classical peak reduction theorem for automorphisms of free groups in the setting of right-angled Artin groups. We use this peak reduction theorem to prove two important corollaries about the action of the automorphism group of a right-angled Artin group AΓ on the set of k–tuples of conjugacy classes from AΓ: orbit membership is decidable, and stabilizers are finitely presentable. Further, we explain procedures for checking orbit membership and building presentations of stabilizers. This improves on a previous result of the author. We overcome a technical difficulty from the previous work by considering infinite generating sets for the automorphism groups. The method also involves a variation on the Hermite normal form for matrices.

Détail

DOI : 10.2140/agt.2014.14.1677

Classification : 20F36, 20F28, 15A36
Keywords: Whitehead algorithm, peak reduction, automorphism groups of groups, right-angled Artin groups, raags, Hermite normal form

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