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Main Authors: Byard, Alexander W., Cai, Brian, Jones, Nathan P., Vuong, Lucy H., Yetter, David N.
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2406.15387
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author Byard, Alexander W.
Cai, Brian
Jones, Nathan P.
Vuong, Lucy H.
Yetter, David N.
author_facet Byard, Alexander W.
Cai, Brian
Jones, Nathan P.
Vuong, Lucy H.
Yetter, David N.
contents We undertake the study of profinite quandles. We provide several constructions of profinite quandles from profinite groups, and from other profinite quandle. We characterize which subquandles of profinite quandles are again profinite. Finally, we provide a characterization of algebraically connected profinite quandles in terms of the profinite completion of their inner automorphism groups $\widehat{\Inn(Q)}$. It is anticipated that the results herein will find applications to the étale homotopy theory of number fields. v.2 has been updated to include an example due to Ariel Davis settling in the negative the question of whether all Stone topological quandles are profinite.
format Preprint
id arxiv_https___arxiv_org_abs_2406_15387
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On Profinite Quandles
Byard, Alexander W.
Cai, Brian
Jones, Nathan P.
Vuong, Lucy H.
Yetter, David N.
Geometric Topology
08A99, 57K12, 20E18
We undertake the study of profinite quandles. We provide several constructions of profinite quandles from profinite groups, and from other profinite quandle. We characterize which subquandles of profinite quandles are again profinite. Finally, we provide a characterization of algebraically connected profinite quandles in terms of the profinite completion of their inner automorphism groups $\widehat{\Inn(Q)}$. It is anticipated that the results herein will find applications to the étale homotopy theory of number fields. v.2 has been updated to include an example due to Ariel Davis settling in the negative the question of whether all Stone topological quandles are profinite.
title On Profinite Quandles
topic Geometric Topology
08A99, 57K12, 20E18
url https://arxiv.org/abs/2406.15387