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configuration-spaces and iterated loop-spaces

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#algebraic-topology #homotopy-theory #monoid #classifying-spaces #loop-spaces
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Is the classifying space a fully faithful functor?

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#algebraic-topology #classifying-spaces
93
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Infinite torsion group with K(G,1) of finite type

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#group-theory #homological-algebra #classifying-spaces
344
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Does a group homomorphism up to homotopy induce a map between classifying spaces?

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#algebraic-topology #homotopy-theory #classifying-spaces
84
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Classifying vector bundles with a reduction of its structure group

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#vector-bundles #principal-bundles #classifying-spaces
1.7k
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The oriented Grassmannian $\widetilde{\text{Gr}}(k,\mathbb{R}^n)$ is simply connected for $n>2$

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#algebraic-topology #grassmannian #classifying-spaces
64
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Cohomology of a classifying space

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#fiber-bundles #characteristic-classes #classifying-spaces
90
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Are there multiple non-isomorphic principal $G$-bundles on Euclidean space?

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#lie-groups #principal-bundles #classifying-spaces #gauge-theory
840
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A category whose classifying space has nontrivial higher homotopy groups

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#algebraic-topology #category-theory #examples-counterexamples #homotopy-theory #classifying-spaces
412
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Relation between two notions of $BG$

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#algebraic-topology #homotopy-theory #classifying-spaces #topological-stacks
671
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Classification of line bundles by group homomorphisms from the fundamental group to $\mathbb{Z}_2$

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#algebraic-topology #homotopy-theory #vector-bundles #fundamental-groups #classifying-spaces
1.1k
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Example of building a classifying space

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#algebraic-topology #homotopy-theory #topological-groups #classifying-spaces
370
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classifying space of a category

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#category-theory #simplicial-stuff #classifying-spaces #k-theory #algebraic-k-theory
276
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Source request for $H^*(B\mathrm{TOP},\mathbb{Q})\cong H^*(BO,\mathbb{Q})$

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#reference-request #algebraic-topology #characteristic-classes #classifying-spaces
416
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How to compare the K-theory and singular cohomology of a classifying space

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#algebraic-topology #homology-cohomology #topological-k-theory #classifying-spaces

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