Loxodromic elements in the cyclic splitting complex and their centralizers
Group Theory
2019-09-18 v2
Abstract
We show that an outer automorphism acts loxodromically on the cyclic splitting complex if and only if it has a filling lamination and no generic leaf of the lamination is carried by a vertex group of a cyclic splitting. This is the analog for the cyclic splitting complex of Handel-Mosher's theorem on loxodromics for the free splitting complex. We also show that such outer automorphisms have virtually cyclic centralizers.
Keywords
Cite
@article{arxiv.1710.10478,
title = {Loxodromic elements in the cyclic splitting complex and their centralizers},
author = {Radhika Gupta and Derrick Wigglesworth},
journal= {arXiv preprint arXiv:1710.10478},
year = {2019}
}
Comments
27 pages, 2 figures. Sections 3 & 4 reorganized and exposition improved. Final version; accepted for publication in Pacific Journal of Mathematics