- #1
Bacle
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- 1
Hi, Everyone:
LetB: E-->X be a line bundle, with scructure group G and X has a CW -decomposition.
I am trying to understand why/how, if the structure group G of B is connected,
then any trivialization over the 0-skeleton of X can be extended to a trivialization
of the 1-skeleton.
I understand that for every k-cell f:D^k --.X (D^k is the k-disk) , the
pullback bundle is trivial (by contractibility of D^k), but I don't see how/why
the connectedness of G alllows us to extend a given trivialization from the
0-skeleton to the 1-skeleton.
There is also a mention of a canonical trivialization over the cells. Anyone
know what that is.?
Thanks.
LetB: E-->X be a line bundle, with scructure group G and X has a CW -decomposition.
I am trying to understand why/how, if the structure group G of B is connected,
then any trivialization over the 0-skeleton of X can be extended to a trivialization
of the 1-skeleton.
I understand that for every k-cell f:D^k --.X (D^k is the k-disk) , the
pullback bundle is trivial (by contractibility of D^k), but I don't see how/why
the connectedness of G alllows us to extend a given trivialization from the
0-skeleton to the 1-skeleton.
There is also a mention of a canonical trivialization over the cells. Anyone
know what that is.?
Thanks.