Volume 14, issue 3 (2014)

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

Volume 19
Issue 6, 2677–3215
Issue 5, 2151–2676
Issue 4, 1619–2150
Issue 3, 1079–1618
Issue 2, 533–1078
Issue 1, 1–532

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

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

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

Matthew B Day

Algebraic & Geometric Topology 14 (2014) 1677–1743
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.

Keywords
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
References
Publication
Received: 5 April 2013
Revised: 19 November 2013
Accepted: 20 November 2013
Published: 29 May 2014
Authors
Matthew B Day
Department of Mathematical Sciences
University of Arkansas
SCEN 301
Fayetteville, AR 72701
United States
http://comp.uark.edu/~matthewd/