Bundles with a lift of infinitesimal diffeomorphisms

Details Bundles with a lift of infinitesimal diffeomorphisms Bundles with a lift of infinitesimal diffeomorphisms

2009-11-18

arxiv.org/abs/0911.3532v1

Mathematics

Differential Geometry

39 pages

Scientific paper

We slightly extend the notion of a natural fibre bundle by requiring diffeomorphisms of the base to lift to automorphisms of the bundle only infinitesimally, i.e. at the level of the Lie algebra of vector fields. Spin structures are natural only in this extended sense. We classify fibre bundles with this property, assuming a finite dimensional structure group. This includes all spin structures, but only some generalised spin structures. This classification links the gauge group G to the topology of space-time.

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