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== | ||
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* ''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'' | ||
* ''Positive scalar curvature with symmetry'' by Bernhard Hanke | * ''Positive scalar curvature with symmetry'' by Bernhard Hanke | ||
* ''Simply connected manifolds of positive scalar curvature'' by Stephan Stolz, ''The Annals of Mathematics, 2nd Ser., Vol. 136, No. 3 (Nov., 1992), pp. 511-540'' | |||
Latest revision as of 19:46, 18 May 2008
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
- Simply connected manifolds of positive scalar curvature by Stephan Stolz, The Annals of Mathematics, 2nd Ser., Vol. 136, No. 3 (Nov., 1992), pp. 511-540