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Results tagged with classifying-spaces
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user 108274
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.
2
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0
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construction of open subsets in classifying space $BG$
Let $G$ be an arbitrary group and we
construct the classifying space $BG$ as quotient
of $EG$ where the latter one is considered in
this discussion to be constructed in natural way as $\Delta$-complex …
- 6,038
4
votes
1
answer
734
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Classifying space BG and contractable space EG
This question is probably not research level that's why I asked it previously on MSE a week ago. Unfortunately it doesn't get much attention there and I thought I would try it here.
Choose a arbitra …
- 6,038
2
votes
0
answers
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Local-to-global philosophy for crossed modules
In the survey Groupoids and crossed objects in algebraic topology Ronald Brown made after Corollary 5.17 (p 30) an very interesting remark I not fully understand. He stated that this
Corollary 5.17 L …
- 6,038
5
votes
0
answers
319
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Čech nerve $C(U)$ corresponds to $BG$ in same manner as a hypercover $\mathcal{H}(U)$ to
We can via the bar construction canonically associate to a monoid $A$ the nerve $N(B A)$, a simplicial set with $N(\mathbf{B}A)_k := \times^{k+1} A $ and canonical face maps and degeneracy maps induc …
- 6,038
5
votes
1
answer
367
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$1$-cocycle associated to universal $G$-bundle $EG \to BG$
Let $G$ be a (topological) group whose identity element $e_G$ is
a nondegenerated basepoint (e.g. if $G$ is a Lie group). Then that's a
known fact that there is for every 'nice' enough topological spa …
- 6,038
5
votes
2
answers
334
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Construct a 'nice' trivializing cover of universal principal $G$-bundle $EG \to BG$
Let G be a discrete or say for sake of simplicity a finite group. In Hatcher's book Algebraic Topology on p 89 the construction of universal bundle $EG$ carries structure of a $\Delta$-complex whose …
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