Volume 2, issue 2 (2002)

Download this article
For printing
Recent Issues

Volume 20
Issue 7, 3219–3760
Issue 6, 2687–3218
Issue 5, 2145–2685
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

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
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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


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.

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