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- W2519773987 abstract "In cite{Ka14} we produced an algorithm for deciding whether or not an element $phiin Out(F_N)$ is an iwip (fully irreducible) automorphism. At several points that algorithm was rather inefficient as it involved some general enumeration procedures as well as running several abstract processes in parallel. In this paper we refine the algorithm from cite{Ka14} by eliminating these inefficient features, and also by eliminating any use of mapping class groups algorithms. Our main result is to produce, for any fixed $Nge 3$, an algorithm which, given a topological representative $f$ of an element $phi$ of $Out(F_N)$, decides in polynomial time in terms of the of $f$, whether or not $phi$ is fully irreducible. In addition, we provide a train track criterion of being fully irreducible which covers all fully irreducible elements of $Out(F_N)$, including both atoroidal and non-atoroidal ones. We also give an algorithm, alternative to that of Turner, for finding all the indivisible Nielsen paths in an expanding train track map, and estimate the complexity of this algorithm. An appendix by Mark Bell provides a polynomial upper bound, in terms of the size of the topological representative, on the complexity of the Bestvina-Handel algorithm cite{BH92} for finding either an irreducible train track representative or a topological reduction." @default.
- W2519773987 created "2016-09-23" @default.
- W2519773987 creator A5023281472 @default.
- W2519773987 date "2016-09-13" @default.
- W2519773987 modified "2023-09-27" @default.
- W2519773987 title "Detecting fully irreducible automorphisms: a polynomial time algorithm. With an appendix by Mark C. Bell" @default.
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