Abstract
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 on the set of –tuples of conjugacy classes from : 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.
Citation
Matthew B Day. "Full-featured peak reduction in right-angled Artin groups." Algebr. Geom. Topol. 14 (3) 1677 - 1743, 2014. https://doi.org/10.2140/agt.2014.14.1677
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