Reference : On the Concept of a Filtered Bundle
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
On the Concept of a Filtered Bundle
Bruce, Andrew mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Grabowska, Katarzyna mailto [University of Warsaw, Poland > Faculty of Physics]
Grabowski, Janusz mailto [Polish Academy of Sciences > Institute of Mathematics]
International Journal of Geometric Methods in Modern Physics
World Scientific
[en] fibre bundles ; graded manifolds ; jet bundles
[en] We present the notion of a filtered bundle as a generalization of a graded bundle. In
particular, we weaken the necessity of the transformation laws for local coordinates
to exactly respect the weight of the coordinates by allowing more general polynomial
transformation laws. The key examples of such bundles include affine bundles and various
jet bundles, both of which play fundamental roles in geometric mechanics and classical
field theory. We also present the notion of double filtered bundles which provide natural
generalizations of double vector bundles and double affine bundles. Furthermore, we show
that the linearization of a filtered bundle — which can be seen as a partial polarization
of the admissible changes of local coordinates — is well defined.
Polish National Science Centre grant under the contract number DEC-2012/06/A/ST1/00256

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