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Results tagged with classifying-spaces
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user 18263
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.
13
votes
1
answer
469
views
When does localization preserve homotopy type of classifying spaces?
Let $\mathcal{C}$ be a small category and $\Sigma$ a collection of morphisms in $\mathcal{C}$. Denote by $F_\Sigma:\mathcal{C} \to \mathcal{C}[\Sigma^{-1}]$ the usual quotient functor from $\mathcal{C …
- 15.5k
5
votes
0
answers
230
views
Adding morphisms to a category without changing homotopy type
I have a really tame category $C$: there are only finitely many objects $C_0$, each hom-set $C(x,y)$ for $x,y \in C_0$ has at most one element, and (aside from identity morphisms) if $C(x,y)$ is non-e …
- 15.5k
3
votes
1
answer
147
views
Classifying space for homology endomorphisms supported on a graph?
Let $X$ be a reasonable topological space (say one that has the homotopy type of a finite CW complex) and consider a subset $\Gamma$ of $X \times X$ so that the projection $p:\Gamma \to X$ onto the fi …
- 15.5k