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The topology of moment-angle manifolds——on a conjecture of S. Gitler and S. López de Medrano

         

摘要

In this paper,we study the topology of moment-angle manifolds and prove a conjecture of S.Gitler and S.Lopez de Medrano concerned with the behavior of the moment-angle manifold under the surgery’cutting off a vertex’on a simple polytope.Let P be a simple polytope of dimension n with m facets and Pv be a poly tope obtained from P by cutting off one vertex v.Let Z=Z(P)and Zv=Z(Pv)be the corresponding moment-angle manifolds.S.Gitler and S.Lopez de Medrano conjectured that:Zv is diffeomorphic to δ[(Z(-D^n+m)×D^2]##^m-n/j=1(m-n/j)(S^j+2×S^m+n-j-1),and they proved the conjecture in the case m<3 n.In this paper we prove the conjecture in the general case.

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