Subtleties concerning conformal tractor bundles

C. Graham; Travis Willse

Open Mathematics (2012)

  • Volume: 10, Issue: 5, page 1721-1732
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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C. Graham, and Travis Willse. "Subtleties concerning conformal tractor bundles." Open Mathematics 10.5 (2012): 1721-1732. <http://eudml.org/doc/269690>.

@article{C2012,
abstract = {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.},
author = {C. Graham, Travis Willse},
journal = {Open Mathematics},
keywords = {Conformal geometry; Parabolic geometry; Tractor bundle; Cartan connection; Associated bundle; conformal geometry; parabolic geometry; tractor bundle; associated bundle},
language = {eng},
number = {5},
pages = {1721-1732},
title = {Subtleties concerning conformal tractor bundles},
url = {http://eudml.org/doc/269690},
volume = {10},
year = {2012},
}

TY - JOUR
AU - C. Graham
AU - Travis Willse
TI - Subtleties concerning conformal tractor bundles
JO - Open Mathematics
PY - 2012
VL - 10
IS - 5
SP - 1721
EP - 1732
AB - 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.
LA - eng
KW - Conformal geometry; Parabolic geometry; Tractor bundle; Cartan connection; Associated bundle; conformal geometry; parabolic geometry; tractor bundle; associated bundle
UR - http://eudml.org/doc/269690
ER -

References

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