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The geometry of generalized loxodromic elements

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.
Publication status:
Not published
Peer review status:
Reviewed (other)

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0003-2195-6071
Series:
arXiv
Acceptance date:
2019-07-11
Source identifiers:
976315
Keywords:
Pubs id:
pubs:976315
UUID:
uuid:fd49e110-ffc7-455c-8184-2328edb0c012
Local pid:
pubs:976315
Deposit date:
2019-07-15

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