| 杨昭.多面体截面和小覆盖的闭子流形[J].数学年刊A辑,2011,32(2):237~244 |
| 多面体截面和小覆盖的闭子流形 |
| Section of Polytope and Closed Submanifold of Small Cover |
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| DOI： |
| 中文关键词: 小覆盖 群作用 多面体 |
| 英文关键词:Small cover Group action Polytope |
| 基金项目:国家自然科学基金(No.10931005); 上海市自然科学基金(No.10ZR1403600)资助的项目 |
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| 中文摘要: |
| 设$\pi:M^{n} \rightarrow P^n$是$P^{n}$上的小覆盖, $S$是$P^{n}$的任意一个$n-1$维截面. 给出了$\pi^{-1}(S)$是$n-1$维闭子流形
(或者两个相互同胚$n-1$维闭子流形的不交并), 以及$\pi^{-1}(S)$是$n-1$维伪流形的充要条件. |
| 英文摘要: |
| Let $\pi:M^{n} \rightarrow P^n$ be a small cover of $P^{n}$, $S$ an $(n-1)$-dimensional section of $P^{n}$. The author deals with the
relationship between $S$ and $\pi^{-1}(S)$, and obtains a necessary and sufficient condition to guarantee that $\pi^{-1}(S)$ is an $(n-1)$-dimensional
closed submanifold (or the disjoint union of two $(n-1)$-dimensional closed submanifolds which are homeomorphic to each other), and a necessary and
sufficient condition to guarantee that $\pi^{-1}(S)$ is an $(n-1)$-dimensional pseudomanifold. |
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