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Results tagged with classifying-spaces
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user 118688
The classifying space BG of a group G classifies principal G-bundles, in that homotopy classes of maps [X, BG] are naturally identified with isomorphism classes of principal G-bundles P ⭢ X.
3
votes
1
answer
473
views
Motivation for classifying vector bundles
The statement I am familiar with regarding classification of vector bundles is :
Given a paracompact space $X$. The set of isomorphism classes of rank $n$ vector bundles over $X$ is in bijective c …
- 6,023
7
votes
1
answer
782
views
Classification of Principal $G$ bundles and vector bundles in smooth sense
Suppose $G$ is a Topological group then classification theorem of Principal $G$ bundles says that
there is a Principal $G$ bundle $EG\rightarrow BG$ such that any principal $G$ bundle over a dece …
- 6,023
2
votes
0
answers
133
views
Associated bundle construction and classifying space
Let $\theta:G\rightarrow H$ be a morphism of Lie groups.
Given $G$ we have classifying space $BG$ and given $H$ we have classifying space $BH$. This $\theta:G\rightarrow H$ gives a map $B\theta:BG\ri …
- 6,023