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2002 Maximal index automorphisms of free groups with no attracting fixed points on the boundary are Dehn twists
Armando Martino
Algebr. Geom. Topol. 2(2): 897-919 (2002). DOI: 10.2140/agt.2002.2.897

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.

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Armando Martino. "Maximal index automorphisms of free groups with no attracting fixed points on the boundary are Dehn twists." Algebr. Geom. Topol. 2 (2) 897 - 919, 2002. https://doi.org/10.2140/agt.2002.2.897

Information

Received: 4 February 2002; Accepted: 21 August 2002; Published: 2002
First available in Project Euclid: 21 December 2017

zbMATH: 1047.20021
MathSciNet: MR1936974
Digital Object Identifier: 10.2140/agt.2002.2.897

Subjects:
Primary: 20E05, 20E36

Rights: Copyright © 2002 Mathematical Sciences Publishers

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