Moment-angle复形轨道构型空间的欧拉示性数

孟媛媛; 王彦英

doi:10.3969/j.issn.1000-5641.2016.06.011

华东师范大学学报（自然科学版） >

2016 , Vol. 2016 >Issue 6: 102 - 110

DOI: https://doi.org/10.3969/j.issn.1000-5641.2016.06.011

数学

Moment-angle复形轨道构型空间的欧拉示性数

孟媛媛 ,
王彦英

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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

网络出版日期: 2017-01-13

基金资助

国家自然科学基金(11426162)

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

MENG Yuan-yuan ,
WANG Yan-ying

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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 date: 2015-12-21

Online published: 2017-01-13

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摘要

设I^m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I^m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(D^d)^m→I^m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F_G(Z _K,d,n). 由F_G(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F_G(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.

关键词：

轨道构型空间; moment-angle复形; 单纯复形; 欧拉示性数

本文引用格式

孟媛媛 , 王彦英 . Moment-angle复形轨道构型空间的欧拉示性数[J]. 华东师范大学学报（自然科学版）, 2016 , 2016(6) : 102 -110 . DOI: 10.3969/j.issn.1000-5641.2016.06.011

Abstract

Let I^m 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 I^m 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 (D^d)^m→I^m. Putting Z _K,d into the framework of orbit configuration spaces, we get the orbit configuration space F_G(Z _K,d,n). By using the famous Inclusion-exclusion Principle and the combinatorial structure of F_G(Z _K,d,n), we obtain the formula for the Euler characteristic of orbit configuration space F_G(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.

Key words：

orbit configuration space; moment-angle complex; simplicial complex; Euler characteristic

参考文献

[ 1 ] GHRIST R. Configuration spaces and braid groups on graphs in robotics [C]//Proceedings of a Conference in Low Dimensional Topology in Honor of Joan S Birman’s 70th Birthday. Providence: Amer Math Soc, 2001: 29-40.
[ 2 ] FARBER M. Invitation to Topological Robotics [M]. Z¨urich: European Mathematical Society, 2008.
[ 3 ] BUCHSTABER V M, PANOV T E. Torus Actions and Their Applications in Topology and Combinatorics [M]. Providence: Amer Math Soc, 2002.
[ 4 ] CHEN J, LU Z, WU J. Orbit configuration spaces of small covers and quasi-toric manifolds [J/OL]. [2016-09-20]. Mathematics, 2011. http://www.oalib.com/paper/3932108#.V-DH8sbNt98.
[ 5 ] BREDON G E. Introduction to Compact Transformation Groups [M]. New York: Academic Press, 1972.
[ 6 ] ALLDAY C, PUPPE V. Cohomological Methods in Transformation Group [M]. Cambridge: Cambridge University Press, 1993.
[ 7 ] LU Z, YU L. On 3-manifolds with locally standard (Z2)3-actions [J]. Topology and its Applications, 2013, 160(4): 586-605.

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