# sphere 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.

Title sphere theorem SphereTheorem 2013-03-22 15:45:35 2013-03-22 15:45:35 juanman (12619) juanman (12619) 11 juanman (12619) Theorem msc 57M35 3Manifolds