| 付鑫.L\"obell多面体上的小覆盖[J].数学年刊A辑,2017,38(2):227~242 |
| L\"obell多面体上的小覆盖 |
| Small Covers Over L\ddot\rm obell Polytopes |
| Received:October 10, 2014 Revised:June 26, 2015 |
| DOI：10.16205/j.cnki.cama.2017.0018 |
| 中文关键词: L"{o}bell polytope, Small cover, Coloring, Equivariant diffeomorphism |
| 英文关键词:L"{o}bell polytope, Small cover, Coloring, Equivariant diffeomorphism |
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| 中文摘要: |
| 计算了L\"{o}bell多面体上的小覆盖的等变微分同胚类的个数.
在1991年, Davis和Januszkiewicz提出了小覆盖的概念,
给出了组合和拓扑间的一种直接联系,
并证明了单凸多面体上的特征映射($\mathbb{Z}_2^n$染色)与该多面体上的小覆盖一一对应.
文中作者给出了L\"{o}bell多面体上的自同构群和染色规律,
结合Burnside引理计算了一般的L\"{o}bell多面体上的小覆盖的等变微分同胚类的个数. |
| 英文摘要: |
| In this paper, the number of equivariant diffeomorphism
classes of small covers over L\"{o}bell polytopes is calculated. The notion of
small cover was introduced by Davis and Januszkiewicz in 1991,
which gives a direct connection between topology and
combinatorics, and it is proved that all small covers over a simple
convex polytope $P^n$ correspond to all characteristic
functions ($\mathbb{Z}_2^n$-colorings) defined on all facets of
$P^n$. The author finds
the automorphism of L\"{o}bell polytopes and the coloring number defined on
them, and calculates the number of
equivariant diffeomorphism classes of small covers over L\"{o}bell
polytopes, with Burnside lemma applied. |
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