Algorithmic constructions of relative train track maps and CTs

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.

有限秩自由群的每个无旋转外自同构都由一种特别有用的相对火车轨道映射（称为CT）来表示。本文的主要结果是，CT的构造可以算法化。我们论证中的一个关键步骤是证明检查一个不变自由因子系统包含于另一个是否是约化的这一过程是可算法化的。文中包含了几个应用，以及一般情况下相对火车轨道映射的算法构造。