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sphere theorem (Theorem)
Theorem 1 (sphere theorem)   If $ M$ is a differentiable orientable 3-manifold such that $ \pi_2(M)$ is not trivial, then there exists an embedding $ S^2\to M$ such that its image homotopy class is not equal to zero.

This theorem was established and proved by C. Papakyriakopoulos in 1957.



"sphere theorem" is owned by juanman. [ full author list (2) ]
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See Also: 3-manifold

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Cross-references: class, homotopy, image, embedding, 3-manifold, orientable, differentiable
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This is version 8 of sphere theorem, born on 2006-03-11, modified 2008-05-01.
Object id is 7714, canonical name is SphereTheorem.
Accessed 1041 times total.

Classification:
AMS MSC57M35 (Manifolds and cell complexes :: Low-dimensional topology :: Dehn's lemma, sphere theorem, loop theorem, asphericity)

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