Full-featured peak reduction in right-angled Artin groups

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Whitehead algorithm, Peak reduction, Automorphism groups of groups, Right-angled Artin groups, Raags, Hermite normal form


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.


Acknowledgement: This research was supported by a grant from the National Science Foundation, award number DMS-120698.