Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 14, Number 3 (2014), 1677-1743.
Full-featured peak reduction in right-angled Artin groups
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.
Algebr. Geom. Topol., Volume 14, Number 3 (2014), 1677-1743.
Received: 5 April 2013
Revised: 19 November 2013
Accepted: 20 November 2013
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F36: Braid groups; Artin groups
Secondary: 20F28: Automorphism groups of groups [See also 20E36] 15A36
Day, Matthew B. Full-featured peak reduction in right-angled Artin groups. Algebr. Geom. Topol. 14 (2014), no. 3, 1677--1743. doi:10.2140/agt.2014.14.1677. https://projecteuclid.org/euclid.agt/1513715917