## Good coverings of Alexandrov spaces

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- by Ayato Mitsuishi and Takao Yamaguchi PDF
- Trans. Amer. Math. Soc.
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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.## References

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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: mitsuishi@fukuoka-u.ac.jp
**Takao Yamaguchi**- Affiliation: Department of mathematics, Kyoto University, Kitashirakawa, Kyoto 606–8502, Japan
- Email: takao@math.kyoto-u.ac.jp
- 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: https://doi.org/10.1090/tran/7849
- MathSciNet review: 4029692