# An algorithm to detect full irreducibility by bounding the volume of periodic free factors

@article{Clay2014AnAT, title={An algorithm to detect full irreducibility by bounding the volume of periodic free factors}, author={Matt Clay and Johanna Mangahas and Alexandra Pettet}, journal={Michigan Mathematical Journal}, year={2014}, volume={64}, pages={279-292} }

We provide an effective algorithm for determining whether an element φ of the outer automorphism group of a free group is fully irreducible. Our method produces a finite list that can be checked for periodic proper free factors.

## 4 Citations

Patterson-Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for Outer space

- Mathematics
- 2014

We quantitatively relate the Patterson-Sullivant currents and generic stretching factors for free group automorphisms to the asymmetric Lipschitz metric on Outer space and to Guirardel's intersection…

Algorithmic constructions of relative train track maps and CTs

- MathematicsGroups, Geometry, and Dynamics
- 2018

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…

Effective Algebraic Detection of the Nielsen–Thurston Classification of Mapping Classes

- Mathematics
- 2013

In this paper, we propose two algorithms for determining the Nielsen–Thurston classification of a mapping class ψ on a surface S. We start with a finite generating set X for the mapping class group…

Detecting Fully Irreducible Automorphisms: A Polynomial Time Algorithm

- Mathematics, Computer ScienceExp. Math.
- 2019

This article produces an algorithm, for any fixed N ⩾ 3, an algorithm which, given a topological representative f of an element ϕ of , decides in polynomial time in terms of the “size” of f, whether or not ϕ is fully irreducible.

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