Building on [BH92, BFH00], we proved in [FH11] that every element ψ of the outer automorphism group of a finite rank free group is represented by a particularly useful relative train track map. In the case that ψ is rotationless (every outer automorphism has a rotationless power), we showed that there is a type of relative train track map, called a CT, satisfying additional properties. The main result of this paper is that the constructions of these relative train tracks can be made algorithmic. A key step in our argument is proving that it is algorithmic to check if an inclusion F⊏F′ of φ-invariant free factor systems is reduced. We also give applications of the main result.
1
Rutgers University, Newark, USA
2
Lehman College, Bronx, USA
Mark Feighn; Michael Handel. Algorithmic constructions of relative train track maps and CTs. Groups, geometry, and dynamics, Tome 12 (2018) no. 3, pp. 1159-1238. doi: 10.4171/ggd/466
@article{10_4171_ggd_466,
author = {Mark Feighn and Michael Handel},
title = {Algorithmic constructions of relative train track maps and {CTs}},
journal = {Groups, geometry, and dynamics},
pages = {1159--1238},
year = {2018},
volume = {12},
number = {3},
doi = {10.4171/ggd/466},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/466/}
}
TY - JOUR
AU - Mark Feighn
AU - Michael Handel
TI - Algorithmic constructions of relative train track maps and CTs
JO - Groups, geometry, and dynamics
PY - 2018
SP - 1159
EP - 1238
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IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/466/
DO - 10.4171/ggd/466
ID - 10_4171_ggd_466
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%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/466/
%R 10.4171/ggd/466
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