Application of good coverings to collapsing Alexandrov spaces

  title={Application of good coverings to collapsing Alexandrov spaces},
  author={Tadashi Fujioka},
  journal={Pacific Journal of Mathematics},
  • Tadashi Fujioka
  • Published 6 October 2020
  • Mathematics
  • Pacific Journal of Mathematics
Let $M$ be an Alexandrov space collapsing to an Alexandrov space $X$ of lower dimension. Suppose $X$ has no proper extremal subsets and let $F$ denote a regular fiber. We slightly improve the result of Perelman to construct an infinitely long exact sequence of homotopy groups and a spectral sequence of cohomology groups for the pair $(M,X,F)$. The proof is an application of the good coverings of Alexandrov spaces introduced by Mitsuishi-Yamaguchi. We also extend this result to each primitive… 

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