On the geometry of the space of fibrations

Details On the geometry of the space of fibrations On the geometry of the space of fibrations

2009-05-04

arxiv.org/abs/0905.0381v2

Mathematics

Differential Geometry

18 pages, 5 figures

Scientific paper

10.1007/s10455-009-9188-2

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

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