Abstract
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.
Original language | English |
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Pages (from-to) | 1689-1713 |
Number of pages | 25 |
Journal | Annales de l'Institut Fourier |
Volume | 70 |
Issue number | 4 |
DOIs | |
Publication status | Published - 15 Apr 2021 |
Bibliographical note
Acknowledgments:The first author was partially supported by the NSF RTG awards DMS-1502553. The second author was supported by the NSF grant DMS-1440140 while the author was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2016 semester, and by a Titchmarsh Research Fellowship from the University of Oxford.
Keywords
- hyperbolicity
- acylindrical hyperbolicity