List questions from algebraic-topology

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Homology of infinite dimensional real projective space given by Tor-functor

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find two topological spaces $Y_1$, $Y_2$ such that $\pi (Y_1)=\pi (Y_2)= (0)$ but $\pi (Y_1 \cup Y_2)\ne (0)$

Published on 26 Mar 2026 - 6:22

233

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Schoen & Yau's proof of the positive-mass theorem: Why is the surface S homeomorphic to $\mathbb{R}^2$?

Published on 25 Mar 2026 - 12:28

83

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Reduced homology group $H_k(S^4 - N^4, \mathbb Z)=H^{4-k}(S^4 - N^4,\mathbb Z)=H_{k-1}(N^4, \mathbb Z)=\mathbb Z^2$?

Published on 25 Mar 2026 - 4:42

42

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Rank of $\ker \partial_i$ for $n$-simplex

Published on 25 Mar 2026 - 15:59

84

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Discrete Morse Function for $n$-simplex

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129

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Same homotopy type as circle

Published on 07 Apr 2026 - 0:24

935

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How is going around the circle once in each direction homotopic to a point?

Published on 26 Mar 2026 - 6:21

66

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Where can I find the proof of Seifert-van Kampen using generators and relations?

Published on 30 Jan 2019 - 14:28

111

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$\mathrm{Οut}(G) = [BG, BG]$?

Published on 05 Apr 2026 - 22:03

107

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The complex topological $K$-theory spectrum is not an $H\mathbb{Z}$-module.

Published on 08 Apr 2026 - 11:42

172

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Cohomology Leray-Serre spectral sequence in case fiber is not connected?

Published on 25 Mar 2026 - 11:32

84

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Extending a monomorphism of bundles, Lemma 7.3, Atiyah, Shapiro

Published on 25 Mar 2026 - 14:26

39

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An isomorphism of vector bundles over a manifold, $K(X)$,

Published on 25 Mar 2026 - 3:07

List Question

Hatcher Exercise 1.2.8

Homology of infinite dimensional real projective space given by Tor-functor

find two topological spaces $Y_1$, $Y_2$ such that $\pi (Y_1)=\pi (Y_2)= (0)$ but $\pi (Y_1 \cup Y_2)\ne (0)$

Schoen & Yau's proof of the positive-mass theorem: Why is the surface S homeomorphic to $\mathbb{R}^2$?

Reduced homology group $H_k(S^4 - N^4, \mathbb Z)=H^{4-k}(S^4 - N^4,\mathbb Z)=H_{k-1}(N^4, \mathbb Z)=\mathbb Z^2$?

Rank of $\ker \partial_i$ for $n$-simplex

Discrete Morse Function for $n$-simplex

Same homotopy type as circle

How is going around the circle once in each direction homotopic to a point?

Where can I find the proof of Seifert-van Kampen using generators and relations?

$\mathrm{Οut}(G) = [BG, BG]$?

The complex topological $K$-theory spectrum is not an $H\mathbb{Z}$-module.

Cohomology Leray-Serre spectral sequence in case fiber is not connected?

Extending a monomorphism of bundles, Lemma 7.3, Atiyah, Shapiro

An isomorphism of vector bundles over a manifold, $K(X)$,

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