# isotopy

Let $M$ and $N$ be manifolds and $I=[0,1]$ the closed unit interval. A smooth map $h:M\times I\to N$ is called an *isotopy* if the restriction^{} map ${h}_{t}:=h(-,t):M\to N$ is an embedding^{} for all $t\in I$.

In particular, a diffeotopy is an isotopy.

Remark. Given an isotopy $h:M\times I\to N$, there exists a diffeotopy $g:N\times I\to N$ such that ${h}_{t}={g}_{t}\circ {h}_{0}$.

Title | isotopy |
---|---|

Canonical name | Isotopy |

Date of creation | 2013-03-22 14:52:49 |

Last modified on | 2013-03-22 14:52:49 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 5 |

Author | rspuzio (6075) |

Entry type | Definition |

Classification | msc 57R52 |

Related topic | ExampleOfMappingClassGroup |

Related topic | Homeotopy |