sphere theorem

Theorem 1 (sphere theorem).

If $M$ is a differentiable orientable 3-manifold such that ${\pi }_{\mathrm{2}}\mathit{}\mathrm{(}M\mathrm{)}$ is not trivial, then there exists an embedding $S^{\mathrm{2}}\mathrm{\to }M$ 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
Canonical name	SphereTheorem
Date of creation	2013-03-22 15:45:35
Last modified on	2013-03-22 15:45:35
Owner	juanman (12619)
Last modified by	juanman (12619)
Numerical id	11
Author	juanman (12619)
Entry type	Theorem
Classification	msc 57M35
Related topic	3Manifolds