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On the geometry of the space of smooth fibrations

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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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Authors and Affiliations

  1. Ludwig-Maximilian Universität, Munich, Germany

    Vincent Humilière

  2. Humbolt Universität zu Berlin, Berlin, Germany

    Nicolas Roy

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  1. Vincent Humilière
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  2. Nicolas Roy
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Correspondence to Nicolas Roy.

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Humilière, V., Roy, N. On the geometry of the space of smooth fibrations. Ann Glob Anal Geom 37, 307–320 (2010). https://doi.org/10.1007/s10455-009-9188-2

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  • DOI: https://doi.org/10.1007/s10455-009-9188-2

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