## Algebraic & Geometric Topology

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

Matthew B Day

#### 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 $AΓ$ 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 14, Number 3 (2014), 1677-1743.

Dates
Revised: 19 November 2013
Accepted: 20 November 2013
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715917

Digital Object Identifier
doi:10.2140/agt.2014.14.1677

Mathematical Reviews number (MathSciNet)
MR3212581

Zentralblatt MATH identifier
1308.20038

Subjects
Primary: 20F36: Braid groups; Artin groups

#### Citation

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

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