# 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 |