Definitions from Wikipedia (Sphere theorem)

▸ noun:  In mathematics, in the topology of 3-manifolds, the sphere theorem of gives conditions for elements of the second homotopy group of a 3-manifold to be represented by embedded spheres.
▸ noun:  In Riemannian geometry, the sphere theorem, also known as the quarter-pinched sphere theorem, strongly restricts the topology of manifolds admitting metrics with a particular curvature bound.


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