Axis bundles in free-by-cyclic groups
Group Theory
2025-06-16 v1 Geometric Topology
Abstract
Given a splitting of a free-by-cyclic group, the associated monodromy acts on outer space preserving Handel and Mosher's "axis bundle." We show that the property of a monodromy having a "lone axis" is non-generic in the sense that the associated splittings are projectively discrete in first cohomology. Additionally, we show that this discreteness statement cannot be promoted to a finiteness statement.
Keywords
Cite
@article{arxiv.2506.11228,
title = {Axis bundles in free-by-cyclic groups},
author = {Maxwell Plummer},
journal= {arXiv preprint arXiv:2506.11228},
year = {2025}
}
Comments
26 pages, 11 figures. Comments welcome!