List questions from homotopy-theory

Published on 13 Apr 2026 - 23:18

30

Views

Term for a graph respecting homotopy class

Published on 14 Apr 2026 - 4:30

30

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Path connectedness of points, but the space isn't $T_1$?

Published on 11 Apr 2026 - 0:56

501

Views

Morse theory: the loop space of $S^n$

Published on 26 Mar 2026 - 21:12

92

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Brown representability for model categories

Published on 11 May 2026 - 6:11

887

Views

Prove that any closed path is $\mathbb C$-contractible.

Published on 14 Apr 2026 - 0:29

39

Views

Order of operations when dealing with paths in a topological space.

Published on 10 Apr 2026 - 17:24

102

Views

A fixed point theorem for the topological $2$-disc

Published on 13 Apr 2026 - 19:53

1.4k

Views

Confusion about free homotopy, based homotopy and homotopy groups

Published on 11 May 2026 - 7:23

94

Views

What is : $ \mu : RK_{}^{ \Gamma } ( \underline{E \Gamma } ) \to K_{} ( C_{r}^* ( \Gamma ) ) $?

Published on 12 Apr 2026 - 17:56

244

Views

Why is $(D^1,S^0)$ not homotopy equivalent to $(\mathbb{R},\mathbb{R}\backslash\{0\})$ in TOP(2)?

Published on 15 Apr 2026 - 23:49

5.4k

Views

Real world uses of homotopy theory

Published on 12 Apr 2026 - 3:24

15.9k

Views

Fundamental group of the double torus

Published on 10 Apr 2026 - 17:05

373

Views

Does contractibility imply contractibility with a basepoint?

Published on 13 Apr 2026 - 4:51

828

Views

Does noncompact manifold or orbifold have the homotopy type,of CW complex?

Published on 15 Apr 2026 - 8:57

List Question

Is every map $\mathbb{T}^2 \to \mathbb{T}^2$ homotopic to the identity surjective?

Term for a graph respecting homotopy class

Path connectedness of points, but the space isn't $T_1$?

Morse theory: the loop space of $S^n$

Brown representability for model categories

Prove that any closed path is $\mathbb C$-contractible.

Order of operations when dealing with paths in a topological space.

A fixed point theorem for the topological $2$-disc

Confusion about free homotopy, based homotopy and homotopy groups

What is : $ \mu : RK_{}^{ \Gamma } ( \underline{E \Gamma } ) \to K_{} ( C_{r}^* ( \Gamma ) ) $?

Why is $(D^1,S^0)$ not homotopy equivalent to $(\mathbb{R},\mathbb{R}\backslash\{0\})$ in TOP(2)?

Real world uses of homotopy theory

Fundamental group of the double torus

Does contractibility imply contractibility with a basepoint?

Does noncompact manifold or orbifold have the homotopy type,of CW complex?

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