2015/08/28 by Ayato Mitsuishi, Mitsuishi, Ayato, Takao Yamaguchi +1
Mathematics · #53C20 #53C23 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.1508.07110
openalex publication_date 2015/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.