Journal of East China Normal University(Natural Sc

Previous Articles     Next Articles

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

RichHTML

7

PDF

638

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.

Key words: