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arXiv · 1508.07110

Good coverings of Alexandrov spaces

Ayato Mitsuishi·Takao Yamaguchi
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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.

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Ayato Mitsuishi, Takao Yamaguchi. 2018-08-01. Good coverings of Alexandrov spaces. https://arxiv.org/abs/1508.07110

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