论文标题
应用良好的覆盖物在崩溃的亚历山德罗夫空间中
Application of good coverings to collapsing Alexandrov spaces
论文作者
论文摘要
令$ m $为Alexandrov的空间，倒在Alexandrov Space $ x $ shof的较低尺寸上。假设$ x $没有适当的极端子集，让$ f $表示普通纤维。我们稍微改善了Perelman的结果，以构建一对$（M，X，F）$的同型组组的无限长序列和频谱序列。证明是对三菱yamaguchi引入的Alexandrov空间的良好覆盖物的应用。我们还将此结果扩展到$ x $的每个原始极端子集。
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 $X$.
