Subtleties Concerning Conformal Tractor Bundles

Details Subtleties Concerning Conformal Tractor Bundles Subtleties Concerning Conformal Tractor Bundles

2012-01-12

arxiv.org/abs/1201.2670v1

Mathematics

Differential Geometry

17 pages

Scientific paper

The realization of tractor bundles as associated bundles in conformal geometry is studied. It is shown that different natural choices of principal bundle with normal Cartan connection corresponding to a given conformal manifold can give rise to topologically distinct associated tractor bundles for the same inducing representation. Consequences for homogeneous models and conformal holonomy are described. A careful presentation is made of background material concerning standard tractor bundles and equivalence between parabolic geometries and underlying structures.

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