Gromov-Lawson theorem on surgery

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