Subtleties concerning conformal tractor bundles

C. Robin Graham; Travis Willse

doi:10.2478/s11533-012-0093-8

Subtleties concerning conformal tractor bundles

C. Robin Graham, Travis Willse

Research output: Contribution to journal › Article › peer-review

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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.

Original language	English
Pages (from-to)	1721-1732
Number of pages	12
Journal	Central European Journal of Mathematics
Volume	10
Issue number	5
DOIs	https://doi.org/10.2478/s11533-012-0093-8
Publication status	Published - Oct 2012

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title = "Subtleties concerning conformal tractor bundles",

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.",

keywords = "Associated bundle, Cartan connection, Conformal geometry, Parabolic geometry, Tractor bundle",

author = "Graham, {C. Robin} and Travis Willse",

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AU - Willse, Travis

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N2 - 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.

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.

KW - Associated bundle

KW - Cartan connection

KW - Conformal geometry

KW - Parabolic geometry

KW - Tractor bundle

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U2 - 10.2478/s11533-012-0093-8

DO - 10.2478/s11533-012-0093-8

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SP - 1721

EP - 1732

JO - Central European Journal of Mathematics

JF - Central European Journal of Mathematics

IS - 5

ER -

Subtleties concerning conformal tractor bundles

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