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arXiv · 1802.03089

The geometry of generalized loxodromic elements

Carolyn R. Abbott·David Hume
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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.

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Carolyn R. Abbott, David Hume. 2018-02-09. The geometry of generalized loxodromic elements. https://arxiv.org/abs/1802.03089

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