Profinite completion of a pseudomanifold equals the Artin-Mazur etale homotopy type of its branched covers, following from existence of enough K(π,1) open dense subspaces.
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A homotopical consequence of branched covers
Profinite completion of a pseudomanifold equals the Artin-Mazur etale homotopy type of its branched covers, following from existence of enough K(π,1) open dense subspaces.