Gromov-Lawson theorem on surgery

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Template:Scalar curvature result

Statement

Let X be a compact manifold which carries a Riemannian metric of positive scalar curvature. Then any compact manifold obtained from X by performing surgery in codimension at least 3, also admits a Riemannian metric of positive scalar curvature.

References

  • The clasification of simply connected manifolds of positive scalar curvature by Mikhail Gromov and H. Blaine Lawson, Jr., The Annals of Mathematics, 2nd Ser., Vol. 111, No. 3 (May, 1980), pp. 423-434