Gromov-Lawson theorem on spin structure: Difference between revisions
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* It has a [[Riemannian metric]] admitting a [[spin structure]] | * It has a [[Riemannian metric]] admitting a [[spin structure]] | ||
* It has a [[Riemannian metric]] with positive [[scalar curvature]] | * It has a [[Riemannian metric]] with positive [[scalar curvature]] | ||
This is a corollary of the [[Gromov-Lawson theorem on surgery]]. | |||
==References== | ==References== | ||
Revision as of 00:54, 8 July 2007
Template:Scalar curvature result
Statement
A closed simply connected manifold of dimension at least 5 satisfies at least one of these two conditions:
- It has a Riemannian metric admitting a spin structure
- It has a Riemannian metric with positive scalar curvature
This is a corollary of the Gromov-Lawson theorem on surgery.
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
- Positive scalar curvature with symmetry by Bernhard Hanke