# irreducible n-manifold

An $n$-manifold^{} (http://planetmath.org/TopologicalManifold) $M$ is called
*irreducible* if for each embedding of a standard $(n-1)$-sphere ${S}^{n-1}$ in
$M$, there is an embedding of a standard $n$-ball (http://planetmath.org/StandardNBall) ${D}^{n}$ in $M$ such that the
image of the boundary $\partial {D}^{n}$ coincides with the image of
${S}^{n-1}$.

In case of dimension three it can be proved that each irreducible 3-manifold is also a prime (http://planetmath.org/Prime3Manifold) 3-manifold.

Title | irreducible n-manifold |
---|---|

Canonical name | IrreducibleNmanifold |

Date of creation | 2013-03-22 16:05:43 |

Last modified on | 2013-03-22 16:05:43 |

Owner | juanman (12619) |

Last modified by | juanman (12619) |

Numerical id | 12 |

Author | juanman (12619) |

Entry type | Definition |

Classification | msc 57N10 |