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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Good coverings of Alexandrov spaces
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by Ayato Mitsuishi and Takao Yamaguchi PDF
Trans. Amer. Math. Soc. 372 (2019), 8107-8130 Request permission


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
  • MR Author ID: 891109
  • Email:
  • Takao Yamaguchi
  • Affiliation: Department of mathematics, Kyoto University, Kitashirakawa, Kyoto 606–8502, Japan
  • Email:
  • 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
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 8107-8130
  • MSC (2010): Primary 53C20; Secondary 53C23
  • DOI:
  • MathSciNet review: 4029692