On the concept of a filtered bundle. (English) Zbl 1390.58002
The authors present filtered bundles, with the prime examples being affine bundles and jet manifolds of sections of a fiber bundle. A filtered bundle is a fiber bundle with typical fiber \(\mathbb{R}^n\) for which the coordinates are assigned weights and the admissible coordinate transformations are polynomial with terms of possibly lower weight. These bundles generalize graded bundles. The authors prove Batchelor-Gawȩdzki-like theorems for filtered bundles, proving that every filtered bundle is isomorphic to a graded bundle (of the same degree) and to a split graded bundle. The authors conclude by discussing the linearization of a filtered bundle and studying double and multiple filtered bundles.
Reviewer: Derek J. Jung (Urbana)
MSC:
| 58A20 | Jets in global analysis |
| 55R10 | Fiber bundles in algebraic topology |
| 16W70 | Filtered associative rings; filtrational and graded techniques |
| 13F20 | Polynomial rings and ideals; rings of integer-valued polynomials |
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