A homotopical consequence of branched covers
Algebraic Topology
2026-04-20 v2 Algebraic Geometry
Geometric Topology
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 open dense subspaces in a pseudomanifold.
Cite
@article{arxiv.2309.05231,
title = {A homotopical consequence of branched covers},
author = {Runjie Hu},
journal= {arXiv preprint arXiv:2309.05231},
year = {2026}
}