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Results tagged with classifying-spaces
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user 9684
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.
12
votes
A question about cohomology of the classifying spaces of compact groups
(Edited per request to add more detail.)
Consider first the case $G = U(n)$. If $S^1 \to U(1)^n \subset U(n)$ is injective, with $H^*(BS^1) = Z[t]$, $H^*(BU(1)^n) = Z[t_1, \dots, t_n]$, $H^*(BU(n)) = …
- 9,263
5
votes
Group completion of a monoid (braid groups)
See Proposition 1 in
McDuff, D.; Segal, G.
Homology fibrations and the "group-completion'' theorem.
Invent. Math. 31 (1975/76), no. 3, 279–284.
- 9,263
15
votes
What is π_1(BG) for an arbitrary topological group $G$?
The first reference in this general area was:
N. E. Steenrod, "Milgram's classifying
space of a topological group", Topology
7 (1968) 349–368.
Working in the category of compactly generated …
- 9,263