Volume 2, issue 2 (2002)

Download this article
For printing
Recent Issues

Volume 24
Issue 9, 4731–5219
Issue 8, 4139–4730
Issue 7, 3571–4137
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

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

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Maximal index automorphisms of free groups with no attracting fixed points on the boundary are Dehn twists

Armando Martino

Algebraic & Geometric Topology 2 (2002) 897–919

arXiv: math.GR/0101130

Abstract

In this paper we define a quantity called the rank of an outer automorphism of a free group which is the same as the index introduced in [D Gaboriau, A Jaeger, G Levitt and M Lustig, An index for counting fixed points for automorphisms of free groups, Duke Math. J. 93 (1998) 425–452] without the count of fixed points on the boundary. We proceed to analyze outer automorphisms of maximal rank and obtain results analogous to those in [D J Collins and E Turner, An automorphism of a free group of finite rank with maximal rank fixed point subgroup fixes a primitive element, J. Pure and Applied Algebra 88 (1993) 43–49]. We also deduce that all such outer automorphisms can be represented by Dehn twists, thus proving the converse to a result in [M M Cohen and M Lustig, The conjugacy problem for Dehn twist automorphisms of free groups, Comment Math. Helv. 74 (1999) 179–200], and indicate a solution to the conjugacy problem when such automorphisms are given in terms of images of a basis, thus providing a moderate extension to the main theorem of Cohen and Lustig by somewhat different methods.

Keywords
free group, automorphism
Mathematical Subject Classification 2000
Primary: 20E05, 20E36
References
Forward citations
Publication
Received: 4 February 2002
Accepted: 21 August 2002
Published: 20 October 2002
Authors
Armando Martino
Department of Mathematics
University College Cork
Cork
Ireland