# handle decomposition

Let ${M}^{n}$ be a smooth, connected, closed $n$ dimensional manifold^{}.
A handle is ${H}_{\lambda}^{n}={B}^{\lambda}\times {B}^{n-\lambda}$ where ${B}^{\lambda}$ is a $\lambda $-ball.

Any such manifold $M$ is diffeomorphic to the union of finitely many such handles where each handle ${H}_{\lambda}^{n}$ is in a one-to-one correspondence with the critical points of $\lambda $ of a Morse function on $M$.

Title | handle decomposition |
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Canonical name | HandleDecomposition |

Date of creation | 2013-03-22 15:21:28 |

Last modified on | 2013-03-22 15:21:28 |

Owner | RobKing (9598) |

Last modified by | RobKing (9598) |

Numerical id | 8 |

Author | RobKing (9598) |

Entry type | Definition |

Classification | msc 57R19 |