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arXiv · 2309.05231

A homotopical consequence of branched covers

Runjie Hu
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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 $K(\pi,1)$ open dense subspaces in a pseudomanifold.

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Runjie Hu. 2023-09-11. A homotopical consequence of branched covers. https://arxiv.org/abs/2309.05231

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