A classifying space $BG$ of a topological group $G$ is the quotient of a weakly contractible space $EG$ by a free action of $G$. When $G$ is a discrete group $BG$ has homotopy type of $K(G,1)$ and (co)homology groups of $BG$ coincide with group cohomology of $G$.
Questions tagged [classifying-spaces]
266 questions
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Can one apply the classifying space functor $B$ more than once?
For a topological monoid $M$, the classifying space $BM$ is at least a pointed topological space as far as I know.
From where to where is the construction $B$ a functor actually? Can I plug in an $A_\infty$ space $M$ or even a $H$-space $M$? What…
Ronald Bernard
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VC dimension of an oriented hyperplane
What is VC dimension (Vapnik-Chervonenkis dimension) of an oriented hyperplane? I know that VC dimension of set of oriented hyperplanes is $n+1$. Is it the same? I came across this question recently... I know VC dimensions of several algorithms but…
Smajl
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quotient of fiber bundles
Let $G$ a topological group and consider $P$ a $G$-fiber bundle over $B$. Let $H$ any subgroup of $G$ and let $Q$ an $H$-fiber bundle over $B$. Let $P/Q$ be quotient over $B$, such that the fiber has $G/H$ structure (no necessary a group structure).…
mathmim
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what is meant by the space $BSU(2)$,
I am aware of the group, $SU(2)$, but I came across a space, $BSU(2)$, but I have no idea of what this stands for?
I noticed that $BSU(2) \cong \mathbb{HP}^\infty$, can any one please explain how is this if this is true?
Eden Zane
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