On the geometry of the space of smooth fibrations |
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Authors: | Vincent Humilière Nicolas Roy |
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Institution: | 1. Ludwig-Maximilian Universit?t, Munich, Germany 2. Humbolt Universit?t zu Berlin, Berlin, Germany
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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. |
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