Some remarks on profinite completion of spaces

Details Some remarks on profinite completion of spaces Some remarks on profinite completion of spaces

2011-04-24

arxiv.org/abs/1104.4659v2

Mathematics

Algebraic Topology

27 pages; final version; to appear in Proceedings for Conferences in Kyoto (October 2010) "Galois-Teichmueller theory and Arit

Scientific paper

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 Teichmueller theory where equivariant completions are applied. Along the way we collect and survey the most important known results about profinite completion of spaces.

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