Reference : On the Concept of a Filtered Bundle |

Scientific journals : Article | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/32603 | |||

On the Concept of a Filtered Bundle | |

English | |

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] | |

2018 | |

International Journal of Geometric Methods in Modern Physics | |

World Scientific | |

15 | |

34 | |

Yes | |

International | |

[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 | |

Researchers | |

http://hdl.handle.net/10993/32603 | |

10.1142/S0219887818500135 |

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