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Annals of Global Analysis and Geometry

, Volume 37, Issue 3, pp 307–320 | Cite as

On the geometry of the space of smooth fibrations

  • Vincent Humilière
  • Nicolas RoyEmail author
Original Paper
  • 50 Downloads

Abstract

We study geometrical aspects of the space of smooth fibrations between two given manifolds M and B, from the point of view of Fréchet geometry. As a first result, we show that any connected component of this space is the base space of a Fréchet-smooth principal bundle with the identity component of the group of diffeomorphisms of M as total space. Second, we prove that the space of fibrations is also itself the total space of a smooth Fréchet principal bundle with structure group the group of diffeomorphisms of the base B.

Keywords

Manifolds of mappings Fibrations Submersions Fréchet manifolds 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Ludwig-Maximilian UniversitätMunichGermany
  2. 2.Humbolt Universität zu BerlinBerlinGermany

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