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

MENG Yuan-yuan; WANG Yan-ying

doi:10.3969/j.issn.1000-5641.2016.06.011

Journal of East China Normal University(Natural Science) >

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

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

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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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

Cite this article

MENG Yuan-yuan , WANG Yan-ying .

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

[J]. Journal of East China Normal University(Natural Science), 2016 , 2016(6) : 102 -110 . DOI: 10.3969/j.issn.1000-5641.2016.06.011

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