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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0093-8,
author = {C. Graham and Travis Willse},
title = {Subtleties concerning conformal tractor bundles},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {1721-1732},
zbl = {1262.53031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0093-8}
}
C. Graham; Travis Willse. Subtleties concerning conformal tractor bundles. Open Mathematics, Tome 10 (2012) pp. 1721-1732. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0093-8/
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