List questions from algebraic-topology

Published on 05 Nov 2018 - 5:18

67

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Prove that $ρ$ induces a continuous function from $S^n → O(n+1)$ and therefore from $\Bbb RP^n → O(n+1)$

Published on 05 Nov 2018 - 8:05

919

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How to show that S^1 is not contractible just by definition without going into Fundamental group.

Published on 05 Nov 2018 - 9:21

66

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All abelian groups are top.groups?

Published on 04 Apr 2026 - 2:25

140

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understanding Thom's theorem for $\mathrm{MU}$ and Milnor-Novikov's result.

Published on 31 Mar 2026 - 13:08

1.6k

Views

Homotopy class of map from torus to sphere?

Published on 28 Mar 2026 - 16:28

86

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$\widetilde{H}_n(CX,X)\cong \widetilde{H}_n(SX) $

Published on 31 Mar 2026 - 13:07

61

Views

Group Actions on $\Bbb R^n$

Published on 25 Mar 2026 - 11:25

81

Views

CW approximation of a topological group

Published on 25 Mar 2026 - 7:49

156

Views

Classifying map for the hyperplane bundle

Published on 27 Mar 2026 - 9:24

110

Views

Cohomology groups $H^(B(\mathbb{Z}_2\ltimes PSU(4)),\mathbb{Z}_2)$ for $\le3$

Published on 25 Mar 2026 - 9:53

57

Views

Existence of certain surfaces in flat riemannian 3-manifold

Published on 27 Mar 2026 - 16:26

35

Views

Framing convergence as a topological question

Published on 06 Nov 2018 - 17:25

96

Views

About Seifert-Van Kampen Theorem

Published on 06 Nov 2018 - 18:32

107

Views

Stiefel-Whitney class of $O(2)$ and $SO(2)$

Published on 28 Mar 2026 - 16:28

List Question

Let $A ∈ SO(n+1)$ and write $τ(A)$ for the induced map $S^n → S^n$. Prove that $τ(A)\simeq id$

Prove that $ρ$ induces a continuous function from $S^n → O(n+1)$ and therefore from $\Bbb RP^n → O(n+1)$

How to show that S^1 is not contractible just by definition without going into Fundamental group.

All abelian groups are top.groups?

understanding Thom's theorem for $\mathrm{MU}$ and Milnor-Novikov's result.

Homotopy class of map from torus to sphere?

$\widetilde{H}_n(CX,X)\cong \widetilde{H}_n(SX) $

Group Actions on $\Bbb R^n$

CW approximation of a topological group

Classifying map for the hyperplane bundle

Cohomology groups $H^(B(\mathbb{Z}_2\ltimes PSU(4)),\mathbb{Z}_2)$ for $\le3$

Existence of certain surfaces in flat riemannian 3-manifold

Framing convergence as a topological question

About Seifert-Van Kampen Theorem

Stiefel-Whitney class of $O(2)$ and $SO(2)$

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