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On the connectivity of level sets of automorphisms of free groups, with applications to decision problems

On the connectivity of level sets of automorphisms of free groups, with applications to decision problems
On the connectivity of level sets of automorphisms of free groups, with applications to decision problems
We show that the level sets of automorphisms of free groups with respect to the Lipschitz metric are connected as subsets of Culler-Vogtmann space. In fact we prove our result in a more general setting of deformation spaces. As applications, give metric solutions of the conjugacy problem for irreducible automorphisms and the detection of reducibility. We additionally prove technical results that may be of independent interest — such as the fact that the set of displacements is well ordered
arXiv
Francaviglia, Stefano
91be45eb-fadf-48ed-abe8-107c65f85c6c
Martino, Armando
65f1ff81-7659-4543-8ee2-0a109be286f1
Francaviglia, Stefano
91be45eb-fadf-48ed-abe8-107c65f85c6c
Martino, Armando
65f1ff81-7659-4543-8ee2-0a109be286f1

[Unknown type: UNSPECIFIED]

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Abstract

We show that the level sets of automorphisms of free groups with respect to the Lipschitz metric are connected as subsets of Culler-Vogtmann space. In fact we prove our result in a more general setting of deformation spaces. As applications, give metric solutions of the conjugacy problem for irreducible automorphisms and the detection of reducibility. We additionally prove technical results that may be of independent interest — such as the fact that the set of displacements is well ordered

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levelset_I_paper_TAMS_revised_final - Accepted Manuscript
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e-pub ahead of print date: 29 March 2017

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Local EPrints ID: 448082
URI: http://eprints.soton.ac.uk/id/eprint/448082
DOI: doi:10.48550/arXiv.1703.09945
PURE UUID: 191b08af-459b-4fbb-9874-c8306a7e0458
ORCID for Armando Martino: ORCID iD orcid.org/0000-0002-5350-3029

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Date deposited: 01 Apr 2021 15:42
Last modified: 17 Mar 2024 03:16

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Author: Stefano Francaviglia
Author: Armando Martino ORCID iD

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