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| LUSTERNIK-SCHNIRELMANN CATEGORY AND EMBEDDING FINITECOVERING MAPS, PRINCIPAL G-BUNDLES INTO BUNDLES |
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Citation： |
Liu Luofei.LUSTERNIK-SCHNIRELMANN CATEGORY AND EMBEDDING FINITECOVERING MAPS, PRINCIPAL G-BUNDLES INTO BUNDLES[J].Chinese Annals of Mathematics B,1996,17(3):317~324 |
| Page view： 0
Net amount： 767 |
Authors： |
Liu Luofei; |
Foundation： |
Project supported by the National Natural Science
%Foundation of China |
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| Abstract： |
The author proves several embedding theorems for finite
covering maps, principal $G$-bundles into bundles. The main resultsare
1. Let $\pi :E\to X$ be a finite covering map, and $X$ a connected locally path-connected paracompact space. If cat$\, X\leq k$, then the finite covering space $\pi :E\to X$ can be embedded into the trivial real $k$-plane bundle.
2. Let $\pi :E\to X$ be a principal $G$-bundle over a paracompact space. If there exists a linear action of $G$ on $F$ ($F=\bold R$ or $\bold C$) and cat$\, X\leq k$, then $\pi :E\to X$ can be embedded into $\xi_1\oplus\cdots\oplus\xi_k$
for any $F$-vector bundles $\xi_i$, $i=1,\cdots ,k$. |
Keywords： |
Lusternik-Schnirelmann category, Finite covering map,
Principal $G$-bundle |
Classification： |
55M30, 57M12, 57S17, 55R25 |
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