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多面体截面和小覆盖的闭子流形 被引量：2

Section of Polytope and Closed Submanifold of Small Cover
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摘要 设π:M^n→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π^(-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π^(-1)(S)是n-1维伪流形的充要条件. Let π^ ： Mn →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 π^-1 （S）, and obtains a necessary and suKicient condition to guarantee that π-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 π-1（S） is an （n - 1）-dimensional pseudomanifold.
作者 杨昭
机构地区 复旦大学数学科学学院
出处 《数学年刊（A辑）》 CSCD 北大核心 2011年第2期237-244,共8页 Chinese Annals of Mathematics
基金 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
关键词 小覆盖 群作用 多面体 Small cover, Group action, Polytope
分类号 O186.1 [理学—基础数学]
  • 相关文献

参考文献10

  • 1Davis M W, Januszkiewicz T. Convex polytopes, Coxeter orbifolds and torus actions [J]. Duke Math Y, 1991, 61:417-454.
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二级参考文献9

  • 1Davis M. W. and Januszkiewicz T., Convex polytopes, Coxeter orbifolds and torus actions [J], Duke Math. J., 1991, 61:417-454.
  • 2Lu Z. and Yu L., Topology types of 3-dimensional small covers [EB/OL], (2007-11-25) [2008-02-10], http://arxiv.org/abs/0710.4496v3.
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  • 6Lu Z., 2-torus manifolds, cobordism and small covers [EB/OL], (2007-01-31) [2008-02- 10], http://arxiv.org/abs/math/0701928.
  • 7Lu Z. and Masuda M., Equivariant classification of 2-torus manifolds [EB/OL], (2008- 02-16) [2008-03-10], http://arxiv.org/abs/0802.2313.
  • 8Bao Z. Q. and Lii Z., Manifolds associated with (Z2)^n-colored regular graphs [EB/OL], (2008-02-12) [2008-03-10], http://arxiv.org/abs/math/0609557.
  • 9Bredon G. E., Introduction to Compact Transformation Groups [M], New York: Academic Press, 1972.

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数学年刊（A辑）
2011年 第2期

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