# prime n-manifold

A n-manifold (http://planetmath.org/TopologicalManifold) $M$ is called if for all the factorizations of $M$, as a connected sum^{} (http://planetmath.org/ConnectedSum2) $M={M}_{1}\mathrm{\#}{M}_{2}$, one finds that one of the factors ${M}_{1}$ or ${M}_{2}$ is the n-sphere ${S}^{n}$.

The importance for 3-manifold is the existence and uniqueness prime decomposition theorem which says: Each 3-manifold can be decomposed as a connected sum of prime manifolds.

Title | prime n-manifold |
---|---|

Canonical name | PrimeNmanifold |

Date of creation | 2013-03-22 16:05:37 |

Last modified on | 2013-03-22 16:05:37 |

Owner | juanman (12619) |

Last modified by | juanman (12619) |

Numerical id | 14 |

Author | juanman (12619) |

Entry type | Feature |

Classification | msc 57N10 |