Gromov-Lawson theorem on surgery: Difference between revisions
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==Statement== | ==Statement== | ||
Let <math>X</math> be a [[compact manifold]] which carries a [[Riemannian metric]] of positive [[scalar curvature]]. Then any manifold obtained from <math>X</math> by performing [[surgery]] in codimension at least 3, also admits a Riemannian metric of positive scalar curvature. | Let <math>X</math> be a [[compact manifold]] which carries a [[Riemannian metric]] of positive [[scalar curvature]]. Then any compact manifold obtained from <math>X</math> by performing [[surgery]] in codimension at least 3, also admits a Riemannian metric of positive scalar curvature. | ||
==References== | ==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'' | * ''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'' | ||
Latest revision as of 19:46, 18 May 2008
Template:Scalar curvature result
Statement
Let be a compact manifold which carries a Riemannian metric of positive scalar curvature. Then any compact manifold obtained from 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