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Cohomology of classifying spaces

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#reference-request #algebraic-topology #classifying-spaces
165
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Can we see the symplectic nature of cotangent bundles through classifying maps.

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#differential-geometry #algebraic-topology #symplectic-geometry #classifying-spaces
1.4k
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Group (co)homology and classyfing spaces

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#group-theory #reference-request #homology-cohomology #group-cohomology #classifying-spaces
285
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Chern-weil theory on the classifying bundle

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#differential-geometry #algebraic-topology #manifolds #characteristic-classes #classifying-spaces
380
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Classifying space of a group

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#group-theory #algebraic-topology #homotopy-theory #fiber-bundles #classifying-spaces
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Is the classifying space $B^nG$ the Eilenberg-MacLane space $K(G, n)$?

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#algebraic-topology #homotopy-theory #classifying-spaces #eilenberg-maclane-spaces
326
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Proving that $\xi$ is a trivial vector bundle iff $\xi \oplus \varepsilon^1$ is trivial

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#vector-bundles #topological-k-theory #classifying-spaces
33
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Prove $K(\mathbb{Z}^n,2) = B\mathbb{T}^n$

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#algebraic-topology #classifying-spaces
58
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Cohomology morphism $H^*(B\mathbb{Z}_2^n,\mathbb{Z}_2) \to H^*(BS\mathbb{Z}_2^n,\mathbb{Z}_2)$

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#algebraic-topology #homology-cohomology #group-cohomology #classifying-spaces
108
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Homotopy Types of Fibrations in Postnikov Tower encoded by Classifing map

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#algebraic-topology #fibration #classifying-spaces
103
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Classification of surface bundles and an isomorphism between $[S^n, BDiff(X)]$ and $\pi_{n-1}(Diff(X))/\pi_0(Diff(X))$

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#algebraic-topology #homotopy-theory #fiber-bundles #classifying-spaces
163
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Pullback of a covering map along the covering map.

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#algebraic-topology #homotopy-theory #covering-spaces #fiber-bundles #classifying-spaces
99
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How to construct an explicit homotopy equivalence between these classifying spaces?

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#algebraic-topology #homotopy-theory #vector-bundles #classifying-spaces
113
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Maps between classifying spaces induced from group homomorphism

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#algebraic-topology #reference-request #classifying-spaces
217
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Classifying Spaces of Matrix Lie Groups

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#algebraic-topology #lie-groups #k-theory #classifying-spaces #eilenberg-maclane-spaces

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