Volume 14, issue 3 (2014)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 4, 1827–2458
Issue 3, 1253–1825
Issue 2, 621–1251
Issue 1, 1–620

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Full-featured peak reduction in right-angled Artin groups

Matthew B Day

Algebraic & Geometric Topology 14 (2014) 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 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.

Whitehead algorithm, peak reduction, automorphism groups of groups, right-angled Artin groups, raags, Hermite normal form
Mathematical Subject Classification 2010
Primary: 20F36
Secondary: 20F28, 15A36
Received: 5 April 2013
Revised: 19 November 2013
Accepted: 20 November 2013
Published: 29 May 2014
Matthew B Day
Department of Mathematical Sciences
University of Arkansas
SCEN 301
Fayetteville, AR 72701
United States