Good coverings of Alexandrov spaces
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Publication:5243099
DOI10.1090/TRAN/7849zbMATH Open1432.53089arXiv1508.07110OpenAlexW2962855474MaRDI QIDQ5243099
Author name not available (Why is that?)
Publication date: 14 November 2019
Published in: (Search for Journal in Brave)
Abstract: In the present paper, we define a notion of good coverings of Alexandrov spaces with curvature bounded below, and prove that every Alexandrov space admits such a good covering and that it has the same homotopy type as the nerve of the good covering. We also prove the stability of the isomorphism classes of the nerves of good coverings in the non-collapsing case. In the proof, we need a version of Perelman's fibration theorem, which is also proved in this paper.
Full work available at URL: https://arxiv.org/abs/1508.07110
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