# Full-featured peak reduction in right-angled Artin groups

@article{Day2014FullfeaturedPR, title={Full-featured peak reduction in right-angled Artin groups}, author={Matthew B. Day}, journal={Algebraic \& Geometric Topology}, year={2014}, volume={14}, pages={1677-1743} }

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 AA on the set of k ‐tuples of conjugacy classes from AA : orbit membership is decidable, and stabilizers are finitely presentable. Further, we explain procedures for checking orbit membership and building…

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