# Application of good coverings to collapsing Alexandrov spaces

@article{Fujioka2020ApplicationOG, title={Application of good coverings to collapsing Alexandrov spaces}, author={Tadashi Fujioka}, journal={Pacific Journal of Mathematics}, year={2020} }

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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