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Results tagged with classifying-spaces
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user 16862
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.
6
votes
Approximation of classifying space BG of compact Lie group G by finite CW complexes
Yes, but non-functorially in the compact Lie group $G$.
In 1951 Norman Steenrod produced the very first model [4, Theorem 19.6] of a $n$-universal space [4, Definition 19.2]. See the equivalence [4, …
- 687
5
votes
Is the Milnor construction contractible
Oliver Straser is correct in that Milnor himself in 1956 [1] only showed his model for $EG$ is weakly contractible (that is, all its homotopy groups vanish) with his coarse topology on the join. (For …
- 687