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Can someone explain how Consider the universal bundle $G\hookrightarrow EG\rightarrow BG$. Is it possible to construct a principal get another bundle $G$-bundle ($G$ is compact Lie group) EG|_{B}$ by restricting $EG$ over a smooth singular $n$-chain k$-chain $B$?B \in H_k(BG)$ ($k\leq n$)? I know it's perfectly fine to restrict $EG$ to a submanifold of $BG$, but what about chains? |
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bundle over a chainCan someone explain how to construct a principal $G$-bundle ($G$ is compact Lie group) over a smooth singular $n$-chain $B$?
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