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Results tagged with classifying-spaces
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user 644
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.
33
votes
0
answers
2k
views
Is there a (discrete) monoid M injecting into its group completion G for which BM is not hom...
For a (discrete) monoid $M$, the classifying space $BM$ is the
geometric realization of the nerve of the one object category whose
hom-set is $M$. (This definition gives the usual classfiying space
wh …
- 5,309
19
votes
1
answer
2k
views
Homotopy fiber of a map between classifying spaces
I'm looking for a reference (and precise hypothesis if more are needed) for the following facts (or a correction, if I'm just plain wrong):
Let $G$ and $H$ be topological groups and $f : G \to H$ be a …
- 5,309