On the concept of a filtered bundle
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2017
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| _version_ | 1866917824882016256 |
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| author | Bruce, Andrew James Grabowska, Katarzyna Grabowski, Janusz |
| author_facet | Bruce, Andrew James Grabowska, Katarzyna Grabowski, Janusz |
| contents | We present the notion of a filtered bundle as a generalisation 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 generalisations of double vector bundles and double affine bundles. Furthermore, we show that the linearisation of a filtered bundle - which can be seen as a partial polarisation of the admissible changes of local coordinates - is well defined. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1707_02490 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | On the concept of a filtered bundle Bruce, Andrew James Grabowska, Katarzyna Grabowski, Janusz Differential Geometry Mathematical Physics 55R10, 58A20, 16W70, 13F20 We present the notion of a filtered bundle as a generalisation 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 generalisations of double vector bundles and double affine bundles. Furthermore, we show that the linearisation of a filtered bundle - which can be seen as a partial polarisation of the admissible changes of local coordinates - is well defined. |
| title | On the concept of a filtered bundle |
| topic | Differential Geometry Mathematical Physics 55R10, 58A20, 16W70, 13F20 |
| url | https://arxiv.org/abs/1707.02490 |