Abstract
In this paper we give a new proof of Micallef–Wang result concerning the stability of positive isotropic curvature under surgeries in codimension n (n is the dimension of the manifold in question). And we show that this property is not true in codimensions ⩽ n−1. We also prove that any finitely presented group can be the fundamental group of a compact n-manifold with positive p-curvature ( p⩽ n−4).
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