# Application of good coverings to collapsing Alexandrov spaces

@article{Fujioka2020ApplicationOG,
title={Application of good coverings to collapsing Alexandrov spaces},
journal={Pacific Journal of Mathematics},
year={2020}
}
• 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…
2 Citations
. We prove that the Euler characteristic of any collapsing Alexandrov space is equal to the sum of the products of the Euler characteristics with compact support of the strata of the limit space and

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