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Why is a finite field considered an étale Eilenberg-Maclane Space?

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#algebraic-geometry #eilenberg-maclane-spaces #etale-homotopy-theory
72
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Problem regarding the extension of a map from a closed subset of a locally compact separable metric space to where the target space is $K(G,n).$

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#general-topology #algebraic-topology #homology-cohomology #eilenberg-maclane-spaces
101
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Hatcher 4.2.19 homotopy group of skeleton of $K(G,1)$

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#algebraic-topology #cw-complexes #higher-homotopy-groups #eilenberg-maclane-spaces
105
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Intuition for killing homology group

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#algebraic-topology #homology-cohomology #intuition #eilenberg-maclane-spaces
41
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Presentations of smooth manifolds

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#abelian-groups #duality-theorems #classifying-spaces #eilenberg-maclane-spaces
881
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$\pi_n(X^n)$ free Abelian?

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#algebraic-topology #homotopy-theory #eilenberg-maclane-spaces
92
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Enumerating fiber bundles with fiber and base first Eilenberg-Maclane spaces

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#algebraic-topology #fiber-bundles #eilenberg-maclane-spaces
539
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Explicit construction of Eilenberg-Maclane spaces with n=1

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#algebraic-topology #homotopy-theory #fundamental-groups #eilenberg-maclane-spaces
269
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How to construct $K(\mathbb{Z}/5\mathbb{Z},1)$?

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#algebraic-topology #homotopy-theory #eilenberg-maclane-spaces
133
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Proof of the isomorphism $[X, \mathbb{R} P^\infty] \cong H^1(X; \mathbb{Z}/2).$

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#algebraic-topology #classifying-spaces #eilenberg-maclane-spaces
457
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"Cohomology classes correspond to homotopy classes of maps to Eilenberg Maclane spaces" and cup product?

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#algebraic-topology #homology-cohomology #eilenberg-maclane-spaces
144
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Relation between cohomology of Eilenberg- MacLane space and product of projective space

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#algebraic-topology #homology-cohomology #eilenberg-maclane-spaces
163
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Eilenberg–Maclane space: nonvanishing cohomology

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#algebraic-topology #homology-cohomology #eilenberg-maclane-spaces
1.2k
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Is there an analogue of Eilenberg-Maclane spaces for homology?

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#algebraic-topology #homology-cohomology #eilenberg-maclane-spaces
197
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Why is $H^*(K(\pi, 1); A) \cong \text{Ext}^*_{\mathbb{Z}[\pi]}(\mathbb{Z}, A)$?

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#algebraic-topology #group-cohomology #eilenberg-maclane-spaces

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