Available on ORBilu since
13 October 2017
Article (Scientific journals)
On the Concept of a Filtered Bundle
Bruce, Andrew; Grabowska, Katarzyna; Grabowski, Janusz
2018In International Journal of Geometric Methods in Modern Physics, 15, p. 34
Peer reviewed


Full Text
Publisher postprint (388.65 kB)

All documents in ORBilu are protected by a user license.

Send to


Keywords :
fibre bundles; graded manifolds; jet bundles
Abstract :
[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.
Disciplines :
Author, co-author :
Bruce, Andrew ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Grabowska, Katarzyna;  University of Warsaw, Poland > Faculty of Physics
Grabowski, Janusz;  Polish Academy of Sciences > Institute of Mathematics
External co-authors :
Language :
Title :
On the Concept of a Filtered Bundle
Publication date :
Journal title :
International Journal of Geometric Methods in Modern Physics
Publisher :
World Scientific
Volume :
Pages :
Peer reviewed :
Peer reviewed
Funders :
Polish National Science Centre grant under the contract number DEC-2012/06/A/ST1/00256


Number of views
54 (12 by Unilu)
Number of downloads
1 (1 by Unilu)

Scopus citations®
Scopus citations®
without self-citations
WoS citations


Similar publications

Contact ORBilu