Volume 16, issue 6 (2016)

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Lone axes in outer space

Lee Mosher and Catherine Pfaff

Algebraic & Geometric Topology 16 (2016) 3385–3418
Abstract

Handel and Mosher define the axis bundle for a fully irreducible outer automorphism in [Mem. Amer. Math. Soc. 1004 (2011)]. We give a necessary and sufficient condition for the axis bundle to consist of a unique periodic fold line. As a consequence, we give a setting, and means for identifying in this setting, when two elements of an outer automorphism group $Out\left({F}_{r}\right)$ have conjugate powers.

Keywords
outer automorphism, fully irreducible, axis bundle, conjugacy problem
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 05E18, 57M07
Publication
Received: 1 September 2015
Revised: 30 April 2016
Accepted: 18 May 2016
Published: 15 December 2016
Authors
 Lee Mosher Department of Mathematics and Computer Science Rutgers University Newark Newark, NJ 07102 United States http://www.andromeda.rutgers.edu/~mosher Catherine Pfaff Department of Mathematics University of California, Santa Barbara South Hall, Room 6607 Santa Barbara, CA 93106 United States http://math.ucsb.edu/~cpfaff/