Affine bundles are affine spaces over modules

Details Affine bundles are affine spaces over modules Affine bundles are affine spaces over modules

2012-01-27

arxiv.org/abs/1201.5812v1

Mathematics

Differential Geometry

13 pages

Scientific paper

We show that the category of affine bundles over a smooth manifold M is equivalent to the category of affine spaces modelled on projective finitely generated C^\infty(M)-modules. Using this equivalence of categories, we are able to give an alternate proof of the main result of [13], showing that the characterization of vector bundles by means of their Lie algebras of homogeneous differential operators also holds for vector bundles of rank 1 and over any base manifolds.

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