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.
Keywords
Whitehead algorithm, peak reduction, automorphism groups of
groups, right-angled Artin groups, raags, Hermite normal
form
