List questions from homology-cohomology

Published on 31 May 2019 - 11:11

42

Views

Is this homology sequence right?

Published on 31 Mar 2026 - 9:19

123

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In “locally contractible” space, cycles are boundaries.

Published on 25 Mar 2026 - 23:09

124

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When $\textrm{Tor}_n^A(-,A/radA)\neq 0$? ($A$ a finite dimensional $K$-algebra)

Published on 25 Mar 2026 - 6:03

64

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$f$ is a cycle since it is a loop, and since $H_1(point) = 0$, $f$ must then be a boundary.

Published on 01 Apr 2026 - 12:59

938

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Different definitions of (co)homology with local coefficients

Published on 02 Jun 2019 - 13:21

131

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What is the relationship between the support of cohomologous forms, possibly in the context of the Poincaré dual?

Published on 26 Mar 2026 - 12:50

30

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complex integration paths

Published on 27 Mar 2026 - 18:26

117

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Group homology in degrees zero and one using the standard resolution

Published on 26 Mar 2026 - 3:11

64

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Why does $H_{n}(\operatorname{Hom}_{R}(M,I_{\ast}(N))=H_{n}(\operatorname{Hom}_{R}(P_{\ast}(M),N))$?

Published on 26 Mar 2026 - 3:13

456

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Serre classes and the Serre spectral sequence

Published on 25 Mar 2026 - 9:22

149

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Why do we want to compute derived functors via forgetful functors though easier?

Published on 25 Mar 2026 - 7:49

133

Views

Cohomology of toric Calabi-Yau manifolds in $d=4$

Published on 26 Mar 2026 - 12:08

873

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Bundle over circle; Monodromy action on cohomology of fiber

Published on 25 Mar 2026 - 23:39

184

Views

Two different spaces with the same fundamental group and homology

Published on 25 Mar 2026 - 12:54

List Question

Closed Poincaré dual, why $\int_M \omega \wedge \eta_S$ and not $\int_M \eta_S \wedge \omega $?

Is this homology sequence right?

In “locally contractible” space, cycles are boundaries.

When $\textrm{Tor}_n^A(-,A/radA)\neq 0$? ($A$ a finite dimensional $K$-algebra)

$f$ is a cycle since it is a loop, and since $H_1(point) = 0$, $f$ must then be a boundary.

Different definitions of (co)homology with local coefficients

What is the relationship between the support of cohomologous forms, possibly in the context of the Poincaré dual?

complex integration paths

Group homology in degrees zero and one using the standard resolution

Why does $H_{n}(\operatorname{Hom}_{R}(M,I_{\ast}(N))=H_{n}(\operatorname{Hom}_{R}(P_{\ast}(M),N))$?

Serre classes and the Serre spectral sequence

Why do we want to compute derived functors via forgetful functors though easier?

Cohomology of toric Calabi-Yau manifolds in $d=4$

Bundle over circle; Monodromy action on cohomology of fiber

Two different spaces with the same fundamental group and homology

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