A homotopical consequence of branched covers
Abstract
We prove that the profinite completion of a pseudomanifold is the Artin-Mazur's etale homotopy type construction on its branched covers, which was implicitly conjectured by Sullivan in his MIT note (page 247) around 1970. This is a consequence of the existence of enough K(π,1) open dense subspaces in a pseudomanifold.
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