# Lone Axes in Outer Space

• Published in 2013
In the collection
Handel and Mosher define the axis bundle for a fully irreducible outer automorphism in "Axes in Outer Space." In this paper 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.

### BibTeX entry

@article{Mosher2013,
title = {Lone Axes in Outer Space},
author = {Mosher, Lee and Pfaff, Catherine},
url = {http://arxiv.org/abs/1311.6855 http://arxiv.org/pdf/1311.6855v3},
urldate = {2013-11-29},
abstract = {Handel and Mosher define the axis bundle for a fully irreducible outer
automorphism in "Axes in Outer Space." In this paper 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.},
comment = {},
month = {nov},
year = 2013,
archivePrefix = {arXiv},
eprint = {1311.6855},
primaryClass = {math.GR},
collections = {Attention-grabbing titles}
}