JournalsggdVol. 12, No. 3pp. 1159–1238

Algorithmic constructions of relative train track maps and CTs

  • Mark Feighn

    Rutgers University, Newark, USA
  • Michael Handel

    Lehman College, Bronx, USA
Algorithmic constructions of relative train track maps and CTs cover
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Abstract

Building on [BH92, BFH00], we proved in [FH11] that every element ψ\psi 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\psi 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 FF\mathcal F \sqsubset \mathcal F' of ϕ\phi-invariant free factor systems is reduced. We also give applications of the main result.

Cite this article

Mark Feighn, Michael Handel, Algorithmic constructions of relative train track maps and CTs. Groups Geom. Dyn. 12 (2018), no. 3, pp. 1159–1238

DOI 10.4171/GGD/466