List questions from algebraic-topology

Published on 11 Apr 2026 - 23:06

82

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Computable homotopy?

Published on 11 Apr 2026 - 19:42

44

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Is an arc $f:[0,1]\to X $ with base point $x_0\in X$ a surjective function?

Published on 15 Apr 2026 - 1:34

78

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Why is $H_1(S^0)=0$?

Published on 15 Apr 2026 - 21:29

42

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Why is $H_i(E_+^n,S^{n-1})\cong H_{i-1}(S^{n-1})?$

Published on 13 Apr 2026 - 9:09

246

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Free Actions of Finite Groups on Surface of Genus $2$

Published on 12 Apr 2026 - 22:40

106

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Prove that there is a bijection between the space of closed paths in X with base point $x_0$ and the set of continuous functions

Published on 13 Apr 2026 - 20:10

68

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If $\mathbb{Z}≅\widetilde{H_0}(\mathbb{R}P^2)⊕\mathbb{Z}$ then $\widetilde{H_0}(\mathbb{R}P^2)=0$?

Published on 12 Apr 2026 - 9:53

38

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Why if $n\geq1$ and $0\leq i\leq j\leq n$ then $F_n^j\circ F_{n-1}^i=F_n^i\circ F_{n-1}^{j-1}$?

Published on 17 Apr 2026 - 7:11

118

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Showing that amphicheirality of 2 knots implies their equivalence.

Published on 14 Apr 2026 - 9:58

242

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Fiber bundle and local trivial fibration

Published on 12 Apr 2026 - 23:39

78

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Identifying triple points of a disc's boundry

Published on 15 Apr 2026 - 10:51

375

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What are the cells of a simplicial complex?

Published on 09 Apr 2026 - 22:16

282

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Interesting topological spaces to calculate the homology groups.

Published on 11 Apr 2026 - 0:18

57

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$\Theta$ is induced by the inclusion map $Z_p\otimes Z_q' \to (C\otimes C')_{p+q}$?

Published on 25 Mar 2026 - 7:45

List Question

Euler characteristic for topological surfaces and triangulations

Computable homotopy?

Is an arc $f:[0,1]\to X $ with base point $x_0\in X$ a surjective function?

Why is $H_1(S^0)=0$?

Why is $H_i(E_+^n,S^{n-1})\cong H_{i-1}(S^{n-1})?$

Free Actions of Finite Groups on Surface of Genus $2$

Prove that there is a bijection between the space of closed paths in X with base point $x_0$ and the set of continuous functions

If $\mathbb{Z}≅\widetilde{H_0}(\mathbb{R}P^2)⊕\mathbb{Z}$ then $\widetilde{H_0}(\mathbb{R}P^2)=0$?

Why if $n\geq1$ and $0\leq i\leq j\leq n$ then $F_n^j\circ F_{n-1}^i=F_n^i\circ F_{n-1}^{j-1}$?

Showing that amphicheirality of 2 knots implies their equivalence.

Fiber bundle and local trivial fibration

Identifying triple points of a disc's boundry

What are the cells of a simplicial complex?

Interesting topological spaces to calculate the homology groups.

$\Theta$ is induced by the inclusion map $Z_p\otimes Z_q' \to (C\otimes C')_{p+q}$?

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