Lone axes in outer space

Mosher, Lee; Pfaff, Catherine

doi:10.2140/agt.2016.16.3385

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Lone axes in outer space

Lee Mosher and Catherine Pfaff

Algebraic & Geometric Topology 16 (2016) 3385–3418

DOI: 10.2140/agt.2016.16.3385

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 $Out (F_{r})$ 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/

Volume 16, issue 6 (2016)