Algorithmic constructions of relative train track maps and CTs

Abstract

Every rotationless outer automorphism of a finite rank free group is represented by a particularly useful relative train track map called a CT. The main result of this paper is that the constructions of CTs can be made algorithmic. A key step in our argument is proving that it is algorithmic to check if an inclusion of one invariant free factor system in another is reduced. Several applications are included, as well as algorithmic constructions for relative train track maps in the general case.