L?bell多面体上的小覆盖

Small Covers Over L?bell Polytopes

计算了L?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(Z^n_2染色)与该多面体上的小覆盖一一对应.文中作者给出了L?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?bell多面体上的小覆盖的等变微分同胚类的个数.

In this paper, the number of equivariant diffeomorphism classes of small covers over LSbell 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 （Z2^n-colorings） defined on all facets of P^n. The author finds the automorphism of LSbell polytopes and the coloring number defined on them, and calculates the number of equivariant diffeomorphism classes of small covers over LSbell polytopes, with Burnside lemma applied.