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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Good coverings of Alexandrov spaces

Authors: Ayato Mitsuishi and Takao Yamaguchi
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 53C20; Secondary 53C23
Published electronically: June 3, 2019
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Abstract: In the present paper, we define a notion of good coverings of Alexandrov spaces with curvature bounded below, and we 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 a kind of stability of the isomorphism classes of the nerves of good coverings in the noncollapsing case. In the proof, we need a version of Perelman's fibration theorem, which is also proved in this paper.

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Additional Information

Ayato Mitsuishi
Affiliation: Department of Applied Mathematics, Fukuoka University, Jyonan-ku, Fukuoka-shi, Fukuoka 814–0180, Japan

Takao Yamaguchi
Affiliation: Department of mathematics, Kyoto University, Kitashirakawa, Kyoto 606–8502, Japan

Received by editor(s): November 12, 2015
Received by editor(s) in revised form: August 1, 2018, and March 12, 2019
Published electronically: June 3, 2019
Additional Notes: This work was supported by JSPS KAKENHI Grant Numbers 26287010, 15H05739, and 15K17529
Article copyright: © Copyright 2019 American Mathematical Society