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Results tagged with classifying-spaces
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user 32022
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
Accepted
Classifying spaces of topological groups whose underlying spaces are homotopy equivalent
As John Klein remarked, the answer to this question will depend on the classifying space functor $B$ one uses.
Let me present one case for which the question can be answered positive which is basical …
- 2,974
8
votes
cohomology of BG, G compact Lie group
Just for completeness, here's another argument without spectral sequences via rational homotopy theory.
Recall a theorem of Hopf, which states that the rational cohomology of a path-connected H-space …
- 2,974
11
votes
Accepted
Characteristic classes of non-linear sphere bundles
For many values of $n$, the answer to both questions is no. Since the fundamental groups of $BX$ and $B\mathrm{Diff}(S^n)$ are finite for $n\ge5$ (This uses that $\pi_0\mathrm{Diff}_\partial(D^n)$ is …
- 2,974