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THE GEOMETRY OF GENERALIZED LOXODROMIC ELEMENTS
Journal article   Peer reviewed

THE GEOMETRY OF GENERALIZED LOXODROMIC ELEMENTS

Carolyn Abbott and David Hume
Annales de l'Institut Fourier, Vol.70(4), pp.1689-1713
01/01/2020

Abstract

Science & Technology Mathematics Physical Sciences
We explore geometric conditions which ensure that 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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