The geometry of generalized loxodromic elements
Group Theory
2019-07-18 v2
Abstract
We explore geometric conditions which ensure a given element of a finitely generated group is, or fails to be, generalized loxodromic; as part of this we prove a generalization of Sisto's result that every generalized loxodromic element is Morse. We provide a sufficient geometric condition for an element of a small cancellation group to be generalized loxodromic in terms of the defining relations and provide a number of constructions which prove that this condition is sharp.
Cite
@article{arxiv.1802.03089,
title = {The geometry of generalized loxodromic elements},
author = {Carolyn R. Abbott and David Hume},
journal= {arXiv preprint arXiv:1802.03089},
year = {2019}
}
Comments
22 pages. To appear in Ann. Inst. Fourier