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 Suyoung Choi ( 최수영 ) , The rational Betti number of small covers and its combinatorics 
 The rational Betti number of small covers and its combinatorics 
 Suyoung Choi ( 최수영 ) 
 Department of Mathematics , Ajou University 
 2013 / 11 / 13 Wednesday 4 PM - 5 PM 
 A small cover is a topological analogue of real toric varieties , and is an important object in toric topology . It is noted that the formula of the ℤ 2 - cohomology ring of small cover is well - known . However , the integral cohomology ring of small covers has not been known well . 
 In this talk , we discuss about the Betti numbers and its torsion of the small covers associated to some nestohedra including graph associahedra . Interestingly , the Betti numbers can be computed by purely combinatorial method ( in terms of graphs and hypergraphs ) . To our surprise , for specific families of graphs , these numbers are deeply related to well - known combinatorial sequences such as the Catalan numbers and Euler zigzag numbers . 
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