Question

How to show that: A path is homotopic to a given point, then it is homotopic to any other point.

score 931 · Answer 1 · 2026-04-13 03:59:43

931

Views

How to show that: A path is homotopic to a given point, then it is homotopic to any other point.

Published on 13 Apr 2026 - 3:59

score 405 · Answer 2 · 2026-04-14 10:17:42

405

Views

Homotopy versus path-homotopy on punctured surface

Published on 14 Apr 2026 - 10:17

score 396 · Answer 3 · 2026-04-14 07:57:25

396

Views

Prove these 3 spaces are homotopy equivalent

Published on 14 Apr 2026 - 7:57

score 1.4k · Answer 4 · 2026-04-13 20:07:57

1.4k

Views

Union of 2-sphere with line segment in $\mathbb{R}^3$ removing one point homotopy equivalence.

Published on 13 Apr 2026 - 20:07

score 62 · Answer 5 · 2026-04-08 22:40:31

62

Views

need help with problem on homology group

Published on 08 Apr 2026 - 22:40

score 1.2k · Answer 6 · 2026-05-11 01:47:09

1.2k

Views

Hopf fibration and $\pi_3(\mathbb{S}^2)$

Published on 11 May 2026 - 1:47

score 332 · Answer 7 · 2026-04-14 04:08:15

332

Views

Why is the Cech nerve $C(U)$ of a surjective map $U\to X$ weakly equivalent to $X$?

Published on 14 Apr 2026 - 4:08

score 928 · Answer 8 · 2026-04-14 02:28:36

928

Views

Is a bijective homotopy equivalence with bijective homotopy inverse a homeomorphism?

Published on 14 Apr 2026 - 2:28

score 215 · Answer 9 · 2026-04-15 06:38:16

215

Views

For which $n$, is any continuous map from $S^n$ to $S^1 \times S^1$ nulhomotopic.

Published on 15 Apr 2026 - 6:38

score 1.8k · Answer 10 · 2026-04-14 15:23:53

1.8k

Views

Two homologous but not homotopic loops on a closed surface of genus greater than one

Published on 14 Apr 2026 - 15:23

score 9.3k · Answer 11 · 2026-04-15 15:04:31

9.3k

Views

Prove homotopic attaching maps give homotopy equivalent spaces by attaching a cell

Published on 15 Apr 2026 - 15:04

score 516 · Answer 12 · 2026-05-06 03:12:27

516

Views

Homotopy groups of some magnetic monopoles

Published on 06 May 2026 - 3:12

score 160 · Answer 13 · 2026-05-06 03:13:40

160

Views

$\pi_n(SU(2)/Z_N)\simeq?$, $\pi_n(SO(3)/Z_N)\simeq?$, $\pi_n(U(1)/Z_N)\simeq?$

Published on 06 May 2026 - 3:13

score 493 · Answer 14 · 2026-04-13 23:51:29

493

Views

Non-closed deformation retract

Published on 13 Apr 2026 - 23:51

score 255 · Answer 15 · 2026-05-15 15:09:23

255

Views

If every finite subcomplex is nullhomotopic, is a simplicial complex contractible?

Published on 15 May 2026 - 15:09

List Question

How to show that: A path is homotopic to a given point, then it is homotopic to any other point.

Homotopy versus path-homotopy on punctured surface

Prove these 3 spaces are homotopy equivalent

Union of 2-sphere with line segment in $\mathbb{R}^3$ removing one point homotopy equivalence.

need help with problem on homology group

Hopf fibration and $\pi_3(\mathbb{S}^2)$

Why is the Cech nerve $C(U)$ of a surjective map $U\to X$ weakly equivalent to $X$?

Is a bijective homotopy equivalence with bijective homotopy inverse a homeomorphism?

For which $n$, is any continuous map from $S^n$ to $S^1 \times S^1$ nulhomotopic.

Two homologous but not homotopic loops on a closed surface of genus greater than one

Prove homotopic attaching maps give homotopy equivalent spaces by attaching a cell

Homotopy groups of some magnetic monopoles

$\pi_n(SU(2)/Z_N)\simeq?$, $\pi_n(SO(3)/Z_N)\simeq?$, $\pi_n(U(1)/Z_N)\simeq?$

Non-closed deformation retract

If every finite subcomplex is nullhomotopic, is a simplicial complex contractible?

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