List questions from algebraic-topology

Published on 20 Mar 2026 - 8:13

134

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A topological question about loops and fixed points

Published on 20 Mar 2026 - 1:37

132

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Proving $\mathcal V(\mathcal I(A)) =A$ and $\mathcal I(\mathcal V(B))= \sqrt{B} $

Published on 22 Mar 2026 - 8:13

110

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Degree of a map $f: S^3 \times S^1 \to S^4$ which is odd with respect to $S^3$

Published on 25 Mar 2026 - 0:02

209

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Face map not well-defined on oriented simplices

Published on 20 Mar 2026 - 0:51

51

Views

Given $f$, does there exist $f_t$ with $f_t(f_{t'}) = f_{t+t'}$ and $f_1 = f$?

Published on 25 Mar 2026 - 0:04

440

Views

Is loop spaces are homotopy equivalent

Published on 22 Mar 2026 - 14:51

62

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confusion on a definition of Genus

Published on 25 Mar 2026 - 1:37

119

Views

Classification of subspaces of $\mathbb{R}^2$ up to homeomorphism

Published on 28 Jan 2018 - 15:13

63

Views

Given $f:X\to Y$, what relation between induced maps $H_k(X) \to H_k(Y)$ and $H^k(Y) \to H^k(X)$?

Published on 28 Jan 2018 - 18:58

171

Views

Non-zero index implies index $1$?

Published on 28 Jan 2018 - 19:03

68

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$f$ has square root if and only if image of $f_*$ contained in $2 \mathbb Z$

Published on 22 Mar 2026 - 13:15

77

Views

Condition induces Null Homotopy

Published on 28 Jan 2018 - 19:50

52

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Pushout commutes with $- \times I$

Published on 28 Jan 2018 - 19:54

289

Views

What is the pushout of $D^n \longleftarrow S^{n-1} \longrightarrow D^n$?

Published on 20 Mar 2026 - 1:52

List Question

Homotopy type of simplicial complexes

A topological question about loops and fixed points

Proving $\mathcal V(\mathcal I(A)) =A$ and $\mathcal I(\mathcal V(B))= \sqrt{B} $

Degree of a map $f: S^3 \times S^1 \to S^4$ which is odd with respect to $S^3$

Face map not well-defined on oriented simplices

Given $f$, does there exist $f_t$ with $f_t(f_{t'}) = f_{t+t'}$ and $f_1 = f$?

Is loop spaces are homotopy equivalent

confusion on a definition of Genus

Classification of subspaces of $\mathbb{R}^2$ up to homeomorphism

Given $f:X\to Y$, what relation between induced maps $H_k(X) \to H_k(Y)$ and $H^k(Y) \to H^k(X)$?

Non-zero index implies index $1$?

$f$ has square root if and only if image of $f_*$ contained in $2 \mathbb Z$

Condition induces Null Homotopy

Pushout commutes with $- \times I$

What is the pushout of $D^n \longleftarrow S^{n-1} \longrightarrow D^n$?

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