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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 Sciences), 2016, (6): 102-110. doi: 10.3969/j.issn.1000-5641.2016.06.011
Citation:
MENG Yuan-yuan, WANG Yan-ying.
The Euler characteristic of orbit configuration space of moment-angle complex
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 Sciences), 2016, (6): 102-110. doi: 10.3969/j.issn.1000-5641.2016.06.011
Citation:
MENG Yuan-yuan, WANG Yan-ying.
The Euler characteristic of orbit configuration space of moment-angle complex
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 complexZ K,d over cc(K) by the pullback of the projection(Dd)mIm. PuttingZ K,d into the framework of orbit configuration spaces, we get the orbit configuration spaceFG(Z K,d,n). By using the famous Inclusion-exclusion Principle and the combinatorial structure ofFG(Z K,d,n), we obtain the formula for the Euler characteristic of orbit configuration spaceFG(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.
[ 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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