The topology of the moment-angle manifolds--On a conjecture of S. Gitler ans S. Lopez

2014/06/26 by Chen, Liman, Fan, Feifei, Wang, Xiangjun
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1406.6756

Abstract

Let P be a simple polytope of dimension n with m facets and P_v be a polytope obtained from P by cutting off one vertex v. Let Z=Z(P) and Z_v=Z(P_v) be the corresponding moment-angle manifolds. In \cite[GL] S.Gitler and S.López conjectured that: Z_v is diffeomorphic to ∂[(Z-int(D^n+m))× D²]\sharp \mathop\sharp _j=1^m-n \binomm-nj (S^j+2× S^m+n-j-1), and they have proved the conjecture in the case m<3n. In this paper we prove the conjecture in general case.

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