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

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 Z_v=Z(P_v) be the corresponding moment-angle manifolds.S.Gitler and S.Lopez de Medrano conjectured that:Z_v is diffeomorphic to ?(Z(-D~(n+m)) × D~2]##_(j=1)~(m-n)(_j~(m-n))(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.