华东师范大学学报(自然科学版)

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Moment-angle复形轨道构型空间的欧拉示性数

孟媛媛[1], 王彦英[2]   

  1. 1. 天津城建大学 理学院 数学系, 天津 300384;
    2. 河北师范大学 数学与信息科学学院, 石家庄 050024
  • 收稿日期:2015-12-21 出版日期:2016-11-25 发布日期:2017-01-13
  • 通讯作者: 孟媛媛, 女, 博士, 讲师, 研究方向为代数拓扑学与微分拓扑学. E-mail: mengyuanyuan815@163.com.
  • 基金资助:
    国家自然科学基金(11426162)

The Euler characteristic of orbit configuration space of moment-angle complex

MENG Yuan-yuan[1], WANG Yan-ying[2]   

  1. 1. Department of Mathematics, School of Science, Tianjin Chengjian University, Tianjin 300384, China;
    2. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China
  • Received:2015-12-21 Online:2016-11-25 Published:2017-01-13

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摘要：

设Im为m维标准方体, K'为单纯复形K的重心重分. 将K'上的锥形按一定规则逐片线性嵌入Im的典范单纯剖分中, 从而得到K对应的一类方体复形cc(K). 根据cc(K)的构造过程, 计算了cc(K)的f-向量, 即各个维数的胞腔个数. 通过投射(Dd)m→Im的拉回, 可定义cc(K)上的moment-angle复形Z K,d. 将Z K,d放入轨道构型空间的框架中, 得到轨道构型空间FG(Z K,d,n). 由FG(Z K,d,n)的组合结构和著名的Inclusion-exclsion原理, 给出了轨道构型空间FG(Z K,d,n)的欧拉示性数利用f-向量表示的计算公式, 并且提供了一种计算Z K,d欧拉示性数的新方法.

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Abstract:

Let Im be the m-dimensional standard cube and K′ the barycentric subdivision of simplicial complex K. There is a PL (piecewise linear) embedding of the cone over K′ to the canonical simplicial subdivision of Im by some rules. Then we obtain a kind of cubical complex cc(K) associated to K. According to the construction of cc(K), we calculate the f-vector of cc(K), i.e., the number of cells in every dimension. There is a definition of moment-angle complex Z K,d over cc(K) by the pullback of the projection (Dd)m→Im. Putting Z K,d into the framework of orbit configuration spaces, we get the orbit configuration space FG(Z K,d,n). By using the famous Inclusion-exclusion Principle and the combinatorial structure of FG(Z K,d,n), we obtain the formula for the Euler characteristic of orbit configuration space FG(Z K,d,n) in terms of f-vector. In addition, we provided a new method of calculating the Euler characteristic of moment-angle complex Z K,d.

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