| Title:
|
On symmetrization of jets (English) |
| Author:
|
Mikulski, W. M. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
157-168 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $F=F^{(A,H,t)}$ and $F^1=F^{(A^1,H^1,t^1)}$ be fiber product preserving bundle functors on the category $\mathcal {FM}_m$ of fibred manifolds $Y$ with $m$-dimensional bases and fibred maps covering local diffeomorphisms. We define a quasi-morphism $(A,H,t)\to (A^1,H^1,t^1)$ to be a $GL(m)$-invariant algebra homomorphism $\nu \colon A\to A^1$ with $t^1=\nu \circ t$. The main result is that there exists an $\mathcal {FM}_m$-natural transformation $FY\to F^1Y$ depending on a classical linear connection on the base of $Y$ if and only if there exists a quasi-morphism $(A,H,t)\to (A^1,H^1,t^1)$. As applications, we study existence problems of symmetrization (holonomization) of higher order jets and of holonomic prolongation of general connections. (English) |
| Keyword:
|
jets |
| Keyword:
|
higher order connections |
| Keyword:
|
Ehresmann prolongation |
| Keyword:
|
Weil functors |
| Keyword:
|
bundle functors |
| Keyword:
|
natural operators |
| MSC:
|
58A05 |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1224.58001 |
| idMR:
|
MR2782766 |
| DOI:
|
10.1007/s10587-011-0004-3 |
| . |
| Date available:
|
2011-05-23T12:38:33Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141525 |
| . |
| Reference:
|
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