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VOL. 63 | 2012 Some remarks on profinite completion of spaces
Gereon Quick

Editor(s) Hiroaki Nakamura, Florian Pop, Leila Schneps, Akio Tamagawa

Abstract

We study profinite completion of spaces in the model category of profinite spaces and construct a rigidification of the completion functors of Artin–Mazur and Sullivan which extends also to non-connected spaces. Another new aspect is an equivariant profinite completion functor and equivariant fibrant replacement functor for a profinite group acting on a space. This is crucial for applications where, for example, Galois groups are involved, or for profinite Teichmüller theory where equivariant completions are applied. Along the way we collect and survey the most important known results of Artin–Mazur, Sullivan and Rector about profinite completion of spaces from a modern point of view. So this article is in part of expository nature.

Information

Published: 1 January 2012
First available in Project Euclid: 24 October 2018

zbMATH: 1321.55008
MathSciNet: MR3051250

Digital Object Identifier: 10.2969/aspm/06310413

Subjects:
Primary: 55P60
Secondary: 14F35, 55Q90

Rights: Copyright © 2012 Mathematical Society of Japan

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