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

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.

[1]  Mark C. Bell.  An algorithm for deciding reducibility , 2014 .

[2]  T. Koberda,et al.  Effective Algebraic Detection of the Nielsen–Thurston Classification of Mapping Classes , 2013, 1312.6141.

[3]  M. Handel,et al.  Subgroup decomposition in Out(F_n), Part II: A relative Kolchin theorem , 2013, 1302.2379.

[4]  Catherine Pfaff.  Ideal Whitehead graphs in Out(Fr) II: the complete graph in each rank , 2013, 1301.6645.

[5]  Ilya Kapovich.  Algorithmic detectability of iwip automorphisms , 2012, 1209.3732.

[6]  Camille Horbez.  Sphere paths in outer space , 2012, 1201.6027.

[7]  M. Calvez.  Fast Nielsen–Thurston classification of braids , 2011, 1112.0165.

[8]  M. Bestvina,et al.  Asymmetry of Outer space , 2009, 0910.5408.

[9]  Yael Algom-Kfir.  Strongly Contracting Geodesics in Outer Space , 2008, 0812.1555.

[10]  Jason A. Behrstock,et al.  Growth of intersection numbers for free group automorphisms , 2008, 0806.4975.

[11]  A. Martino,et al.  METRIC PROPERTIES OF OUTER SPACE , 2008, 0803.0640.

[12]  M. Handel,et al.  The Recognition Theorem for Out(F_n) , 2006, math/0612702.

[13]  Vincent Guirardel.  Cœur et nombre d'intersection pour les actions de groupes sur les arbres , 2005 .

[14]  M. Handel,et al.  The expansion factors of an outer automorphism and its inverse , 2004, math/0410015.

[15]  K. Vogtmann.  Automorphisms of Free Groups and Outer Space , 2002 .

[16]  Michael Handel,et al.  Laminations, trees, and irreducible automorphisms of free groups , 1997 .

[17]  Hessam Hamidi-Tehrani,et al.  Surface diffeomorphisms via train-tracks , 1996 .

[18]  A. Hatcher,et al.  Homological stability for automorphism groups of free groups , 1995 .

[19]  Andrew J. Duncan,et al.  Finding indivisible Nielsen paths for a train track map , 1994 .

[20]  Jérôme E. Los,et al.  Pseudo-Anosov Maps and Invariant Train Tracks in the Disc: A Finite Algorithm , 1993 .

[21]  John R. Stallings,et al.  Topology of finite graphs , 1983 .

[22]  J. Whitehead,et al.  On Equivalent Sets of Elements in a Free Group , 1936 .

[23]  Mladen Bestvina,et al.  Train-tracks for surface homeomorphisms , 1995 .

[24]  R. Hain,et al.  Mapping Class Groups and Moduli Spaces of Riemann Surfaces , 1993 .

[25]  Mladen Bestvina,et al.  Train tracks and automorphisms of free groups , 1992 .

[26]  F. Laudenbach.  Topologie de la dimension trois : homotopie et isotopie , 1974 .

[27]  F. Laudenbach.  Sur Les 2-Spheres D'une Variete de Dimension 3 , 1973 .