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arXiv · 2010.02520

Application of good coverings to collapsing Alexandrov spaces

Tadashi Fujioka
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Abstract

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 extremal subset of $X$.

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Tadashi Fujioka. 2020-10-06. Application of good coverings to collapsing Alexandrov spaces. https://doi.org/10.2140/pjm.2022.316.335

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