### Abstract

This chapter contains foundational material on spaces of diffeomorphisms and embeddings. Such spaces are known to be Fréchet manifolds, separable when the manifolds involved are compact. Versions of these and related facts are developed for manifolds with boundary, as well as in the context of fiber-preserving diffeomorphisms and maps. The latter utilizes a modification of the exponential map, called the aligned exponential, adapted to the fibered structure.

Original language | English |
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Title of host publication | Diffeomorphisms of Elliptic 3-Manifolds |

Publisher | Springer Verlag |

Pages | 9-17 |

Number of pages | 9 |

ISBN (Print) | 9783642315633 |

DOIs | |

Publication status | Published - 2012 Jan 1 |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 2055 |

ISSN (Print) | 0075-8434 |

ISSN (Electronic) | 1617-9692 |

### Keywords

- Homotopy Type
- Horizontal Lift
- Horizontal Part
- Local Chart
- Vector Field

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Hong, S., Kalliongis, J., McCullough, D., & Rubinstein, J. H. (2012). Diffeomorphisms and Embeddings of Manifolds. In

*Diffeomorphisms of Elliptic 3-Manifolds*(pp. 9-17). (Lecture Notes in Mathematics; Vol. 2055). Springer Verlag. https://doi.org/10.1007/978-3-642-31564-0_2