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Results tagged with classifying-spaces
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user 2039
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.
7
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Accepted
What does the classifying space of a topological monoid classify?
Section 5 of Segal's Classifying spaces related to foliations shows that for discrete monoids $M$ the space $BM$ still classifies principal $M$-bundles (in a suitable sense). In Moerdijk's Classifying …
- 12.1k
40
votes
‘Naturally occurring’ $K(\pi, n)$ spaces, for $n \geq 2$
$\DeclareMathOperator\B{B}\newcommand\TOP{\mathrm{TOP}}\newcommand\PL{\mathrm{PL}}\newcommand\BTOP{{\B}\TOP}\newcommand\BPL{{\B}\PL}$Let $\BTOP$ and $\BPL$ be the classifying spaces of topological/PL- …
- 12.1k