English

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.

Keywords

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

R2 v1 2026-06-23T00:16:34.579Z