| Title:
|
On principal connection like bundles (English) |
| Author:
|
Mikulski, Włodzimierz M. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
961-967 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\mathcal {P}\mathcal {B}_m$ be the category of all principal fibred bundles with $m$-dimensional bases and their principal bundle homomorphisms covering embeddings. We introduce the concept of the so called $(r,m)$-systems and describe all gauge bundle functors on $\mathcal {P}\mathcal {B}_m$ of order $r$ by means of the $(r,m)$-systems. Next we present several interesting examples of fiber product preserving gauge bundle functors on $\mathcal {P}\mathcal {B}_m$ of order $r$. Finally, we introduce the concept of product preserving $(r,m)$-systems and describe all fiber product preserving gauge bundle functors on $\mathcal {P}\mathcal {B}_m$ of order $r$ by means of the product preserving $(r,m)$-systems. (English) |
| Keyword:
|
principal bundle |
| Keyword:
|
principal connection |
| Keyword:
|
gauge bundle functor |
| Keyword:
|
natural transformation |
| MSC:
|
58A05 |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 06433707 |
| idMR:
|
MR3304791 |
| DOI:
|
10.1007/s10587-014-0146-1 |
| . |
| Date available:
|
2015-02-09T17:30:38Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144154 |
| . |
| Reference:
|
[1] Doupovec, M., Kolář, I.: Iteration of fiber product preserving bundle functors.Monatsh. Math. 134 (2001), 39-50. MR 1872045, 10.1007/s006050170010 |
| Reference:
|
[2] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry.Springer, Berlin (1993). MR 1202431 |
| Reference:
|
[3] Kolář, I., Mikulski, W. M.: On the fiber product preserving bundle functors.Differ. Geom. Appl. 11 (1999), 105-115. MR 1712139, 10.1016/S0926-2245(99)00022-4 |
| Reference:
|
[4] Mikulski, W. M.: Product preserving gauge bundle functors on all principal bundle homomorphisms.Ann. Pol. Math. 101 (2011), 163-207. Zbl 1219.58001, MR 2785889, 10.4064/ap101-2-6 |
| Reference:
|
[5] Mikulski, W. M.: On the fiber product preserving gauge bundle functors on vector bundles.Ann. Pol. Math. 82 (2003), 251-264. Zbl 1126.58300, MR 2040810, 10.4064/ap82-3-6 |
| . |
