List questions from de-rham-cohomology

Published on 10 Mar 2021 - 21:01

131

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How to see that existence non-trivial parallel $p$-form implies $b_p\geq 1$ using De Rham cohomology?

Published on 16 Mar 2021 - 15:43

297

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Poincaré's take on Poincaré duality before the advent of cohomology?

Published on 23 Feb 2026 - 5:47

41

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How to define integrals for (U(1) valued) compact variables on a circle S1

Published on 06 Apr 2021 - 5:38

40

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What is a presentation for the Rham cohomology of a smooth manifold

Published on 20 Apr 2021 - 23:44

109

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Prove $H^{k}_\text{deRham} (M \times S^{n}) \cong H^{k}_\text{deRham} (M) \bigoplus H^{k-n}_\text{deRham} (M)$ using Mayer-Vietoris

Published on 23 Apr 2021 - 14:12

90

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Example of two non-homeomorphic spaces with the same de Rham group

Published on 23 Apr 2021 - 22:32

78

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In which sense is quantum cohomology a deformation of cohomology?

Published on 24 Apr 2021 - 9:44

185

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Is true that a closed $k$-form defined on an open connected set is exact iff its integral on a compact $k$-manifold without boundary is zero?

Published on 29 Apr 2021 - 7:27

527

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Why the De Rham cohomology just a topological invariant？

Published on 03 May 2021 - 8:19

49

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Help proving locally constant presheaf is constant

Published on 06 May 2021 - 17:23

198

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Computing cohomology over a presheaf

Published on 10 May 2021 - 20:54

319

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Is there a name for this constant associated to smooth maps between spheres? (not degree)

Published on 18 May 2021 - 19:54

145

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Why non closed differential forms do not play important role for the topology of a manifold?

Published on 23 May 2021 - 18:17

58

Views

Show that $P(V^{})$ may be interpreted as the set of all hyperplanes in $V$ ($V^{}=\operatorname{Hom}(V,\mathbb{R}))$

Published on 25 May 2021 - 18:22

List Question

About the existence of homotopy operator

How to see that existence non-trivial parallel $p$-form implies $b_p\geq 1$ using De Rham cohomology?

Poincaré's take on Poincaré duality before the advent of cohomology?

How to define integrals for (U(1) valued) compact variables on a circle S1

What is a presentation for the Rham cohomology of a smooth manifold

Prove $H^{k}_\text{deRham} (M \times S^{n}) \cong H^{k}_\text{deRham} (M) \bigoplus H^{k-n}_\text{deRham} (M)$ using Mayer-Vietoris

Example of two non-homeomorphic spaces with the same de Rham group

In which sense is quantum cohomology a deformation of cohomology?

Is true that a closed $k$-form defined on an open connected set is exact iff its integral on a compact $k$-manifold without boundary is zero?

Why the De Rham cohomology just a topological invariant？

Help proving locally constant presheaf is constant

Computing cohomology over a presheaf

Is there a name for this constant associated to smooth maps between spheres? (not degree)

Why non closed differential forms do not play important role for the topology of a manifold?

Show that $P(V^{})$ may be interpreted as the set of all hyperplanes in $V$ ($V^{}=\operatorname{Hom}(V,\mathbb{R}))$

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