Illinois Journal of Mathematics

Long turns, INP’s and indices for free group automorphisms

Thierry Coulbois and Martin Lustig

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The goal of this paper is to introduce a new tool, called long turns, which is a useful addition to the train track technology for automorphisms of free groups, in that it allows one to control periodic INPs in a train track map and hence the index of the induced automorphism.

Article information

Illinois J. Math., Volume 59, Number 4 (2015), 1087-1109.

Received: 2 May 2016
Revised: 12 May 2016
First available in Project Euclid: 27 February 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20E05: Free nonabelian groups 20E08: Groups acting on trees [See also 20F65] 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 57R30: Foliations; geometric theory


Coulbois, Thierry; Lustig, Martin. Long turns, INP’s and indices for free group automorphisms. Illinois J. Math. 59 (2015), no. 4, 1087--1109. doi:10.1215/ijm/1488186022.

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