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Is the classifying space of a non-compact Lie group equal the classifying space of the maximal compact subgroup?

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#algebraic-topology #lie-groups #homology-cohomology #group-cohomology #classifying-spaces
71
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Finding a cochain with specific coboundary

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#algebraic-topology #homology-cohomology
78
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Symmetric fibre product and Euler classes

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#homology-cohomology #spheres #fiber-bundles #characteristic-classes
166
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Connected components of an open subset

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#algebraic-geometry #homology-cohomology #connectedness #dimension-theory-algebra
127
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Question about a proof establishing how many lines meet $ 4 $ general lines?

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#algebraic-geometry #homology-cohomology #intersection-theory
295
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Exercise 7.7.3 in Weibel (computation of $H^3(\mathfrak{sl}_2,k)$ via Chevalley-Eilenberg complex)

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#lie-algebras #homology-cohomology
52
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reduced homologies of shifted complexes

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#homology-cohomology #simplicial-complex
265
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Example of Mayer-Vietoris sequence

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#algebraic-topology #homology-cohomology #exact-sequence
52
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Chain complex of free $k[x.y]$ modules with strange homology group

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#examples-counterexamples #homology-cohomology #homological-algebra
28
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Low-dimensional subcomplexes, isomorphisms in cohomology?

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#manifolds #homology-cohomology #simplicial-complex
276
Views

How can a point on an elliptic curve be considered a galois cohomology class?

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#number-theory #homology-cohomology #elliptic-curves #group-cohomology #galois-cohomology
42
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Higher torsions ($n$-torsions) in algebraic topology

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#algebraic-topology #homology-cohomology #topological-groups #group-cohomology
93
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Isomorphism of homology chain groups

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#algebraic-topology #homology-cohomology #exact-sequence
436
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Cohomolgoy of $S^1$-bundle over genus $g$ surface

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#algebraic-topology #homology-cohomology #fiber-bundles #spectral-sequences
59
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Meaning of $H_0(X) = \tilde H_0(K)\oplus\Bbb Z $ and its Proof

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#homology-cohomology

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