List questions from homotopy-theory

Published on 17 Apr 2026 - 4:15

371

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principal bundle morphism preserves fundamental group

Published on 27 Mar 2026 - 8:41

445

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Reference request: Inclusion of smooth maps into continuous maps between smooth manifolds is a weak homotopy equivalence.

Published on 28 Apr 2026 - 21:48

1.3k

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How to prove a bundle map is a bundle isomorphism?

Published on 14 Apr 2026 - 2:02

561

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Homotopic retract vs deformation retract

Published on 15 Apr 2026 - 8:03

186

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What does 'equating the like-power of $q$' mean?

Published on 11 Apr 2026 - 18:53

67

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Definition of G-crossed complex.

Published on 12 Apr 2026 - 8:19

340

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Homotopy 'diagrams' for Klein bottle and projective plane

Published on 25 Mar 2026 - 19:04

1.7k

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What is wrong with this proof that the identity map of $S^1$ is nullhomotopic?

Published on 11 Apr 2026 - 21:34

180

Views

Is $(0,1)$ homotopic to $(0,1) \times (0,1)$?

Published on 10 Apr 2026 - 5:53

137

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"Representability" of $\pi_1:\mathsf{hTop}_\ast \longrightarrow \mathsf{Grp}$?

Published on 27 Mar 2026 - 23:28

719

Views

Why is the homotopy category actually important?

Published on 15 Apr 2026 - 20:44

1.6k

Views

Homotopy-invariance of sheaf cohomology for locally constant sheaves

Published on 27 Mar 2026 - 21:03

154

Views

Does the homotopy category functor $\mathsf{Top}_\ast\rightarrow \mathsf{hTop}_\ast$ create products?

Published on 15 Apr 2026 - 20:53

408

Views

when a space is a product of eilenberg mclane spaces for $\pi_1(X)$ is not abelian

Published on 13 Apr 2026 - 8:31

List Question

A Natural Question When Reading Van Kampen Theorem

principal bundle morphism preserves fundamental group

Reference request: Inclusion of smooth maps into continuous maps between smooth manifolds is a weak homotopy equivalence.

How to prove a bundle map is a bundle isomorphism?

Homotopic retract vs deformation retract

What does 'equating the like-power of $q$' mean?

Definition of G-crossed complex.

Homotopy 'diagrams' for Klein bottle and projective plane

What is wrong with this proof that the identity map of $S^1$ is nullhomotopic?

Is $(0,1)$ homotopic to $(0,1) \times (0,1)$?

"Representability" of $\pi_1:\mathsf{hTop}_\ast \longrightarrow \mathsf{Grp}$?

Why is the homotopy category actually important?

Homotopy-invariance of sheaf cohomology for locally constant sheaves

Does the homotopy category functor $\mathsf{Top}_\ast\rightarrow \mathsf{hTop}_\ast$ create products?

when a space is a product of eilenberg mclane spaces for $\pi_1(X)$ is not abelian

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