List questions from algebraic-topology

Published on 14 Apr 2026 - 5:20

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Prerequisites for discrete Morse theory

Published on 25 Mar 2026 - 6:10

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Can the length of a module be seen as a specific Krull-dimension?

Published on 13 Apr 2026 - 12:12

169

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Common refinement of CW complexes

Published on 12 Apr 2026 - 10:59

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Suppose that $X$ is a topological space and $x_0\in X$. Prove that $\widetilde{H_n}(X)=H_n(X,x_0)$ for all $n\geq 0$.

Published on 15 Apr 2026 - 23:20

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If $f,g:(X,A)\to (Y,B)$ are homotopic functions under a homotopy $H:X\times [0,1]\to Y$ then $f_=g_:H_n(X,A)\to H_n(Y,B)$.

Published on 13 Apr 2026 - 22:08

67

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Induced map well defined on coset space of Lie groups.

Published on 25 Mar 2026 - 6:03

82

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Exercise of VII 5.2 Massey's Algebraic Topology.

Published on 15 Apr 2026 - 15:37

994

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Essential closed curves and orientation preserving homeomorphism

Published on 25 Mar 2026 - 4:39

140

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Why $H_1(SX)\cong \widetilde{H_0}(X)$?

Published on 14 Apr 2026 - 7:00

121

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What happens if we remove the point of origin from the moebius band?

Published on 14 Apr 2026 - 20:42

229

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Every Cech cocycle can be represented by a normalised cocycle.

Published on 15 Apr 2026 - 13:15

539

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Is $H_n(X,A)$ naturally isomorphic to $\tilde{H}_n(X/A)$?

Published on 25 Mar 2026 - 9:28

1.5k

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The calculation of a homology group

Published on 11 Apr 2026 - 6:43

149

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Homology and cohomology of manifolds

Published on 11 Apr 2026 - 3:24

List Question

Poset map and fibration

Prerequisites for discrete Morse theory

Can the length of a module be seen as a specific Krull-dimension?

Common refinement of CW complexes

Suppose that $X$ is a topological space and $x_0\in X$. Prove that $\widetilde{H_n}(X)=H_n(X,x_0)$ for all $n\geq 0$.

If $f,g:(X,A)\to (Y,B)$ are homotopic functions under a homotopy $H:X\times [0,1]\to Y$ then $f_=g_:H_n(X,A)\to H_n(Y,B)$.

Induced map well defined on coset space of Lie groups.

Exercise of VII 5.2 Massey's Algebraic Topology.

Essential closed curves and orientation preserving homeomorphism

Why $H_1(SX)\cong \widetilde{H_0}(X)$?

What happens if we remove the point of origin from the moebius band?

Every Cech cocycle can be represented by a normalised cocycle.

Is $H_n(X,A)$ naturally isomorphic to $\tilde{H}_n(X/A)$?

The calculation of a homology group

Homology and cohomology of manifolds

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