Application of good coverings to collapsing Alexandrov spaces
Application of good coverings to collapsing Alexandrov spaces
复制标题
DOI：
10.2140/pjm.2022.316.335
复制
发表时间：
2020-10
影响因子：
0.6
通讯作者：
Tadashi Fujioka
中科院分区：
文献类型：
--
作者：
Tadashi Fujioka
设$M$是一个坍缩为低维的亚历山德罗夫空间$X$的亚历山德罗夫空间。设$X$没有真极值子集，$F$表示正则纤维。本文对Perelman的结果作了一些改进，构造了$（M，X，F）$的同伦群的无穷长正合序列和上同调群的谱序列.证明是Mitsuishi-Yamaguchi引入的Alexandrov空间的好覆盖的应用。我们也将这个结果推广到X的每个本原极值子集。
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 $X$.