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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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(Fr) have conjugate powers.

Keywords
outer automorphism, fully irreducible, axis bundle, conjugacy problem
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 05E18, 57M07
References
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/