Decomposition des varietes affines

Abstract

We associate to a finite cover ( M′,∇′) of a compact connected affine manifold ( M,∇) such that Aff( M,∇) 0 is not solvable, a field K ( K is the real, complex or quaternionic field) and an affine K-transverse foliation F U . Let p=codim K F U, if p>1, we show that ( M′,∇′) or his K-blowing-up along an affine submanifold is a total space of a fibration over P K 1( K p ). We give a partial classification of the manifolds ( M′,∇′) if p=1. We also determine the differentiable structure of 3 and 4-affine manifolds (up to a finite cover) such that Aff( M,∇) 0 is not solvable.