Loxodromic elements in the cyclic splitting complex and their centralizers
arXiv:1710.10478 · doi:10.2140/pjm.2019.301.107
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.
27 pages, 2 figures. Sections 3 & 4 reorganized and exposition improved. Final version; accepted for publication in Pacific Journal of Mathematics