On the geometry of the space of fibrations

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Date
2009-03-09MFO Scientific Program
Research in Pairs 2009Series
Oberwolfach Preprints;2009,15Author
Humilière, Vincent
Roy, Nicolas
Metadata
Show full item recordOWP-2009-15
Abstract
We study geometrical aspects of the space of 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 $B$ .