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Results tagged with classifying-spaces
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user 102519
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.
20
votes
Accepted
Sullivan conjecture for compact Lie groups
You were right to single out Lie groups as potentially interesting. In [Topology 5 (1966), 241-243], Brayton Gray showed that the homotopy group of maps $[BS^1, S^3]$ was uncountable. Indeed, he sho …
- 11.2k
4
votes
non-simple local coefficient system on a fibration of classifying spaces
Lie groups include finite groups. Here is likely the simplest example.
Let $H = C_3$ be the cyclic subgroup of order 3 in the symmetric group $G = S_3$, so $S_3/C_3 = C_2$. So your fiber bundle is …
- 11.2k
2
votes
CW-presentation of configurations of points in plane and space
Here is the original paper by Fox and Neuwirth:
Fox, R.; Neuwirth, L. The braid groups. Math. Scand. 10 (1962), 119–126.
I remember reading this in the late 1970's in grad school, and found it clear …
- 11.2k