Question

Compute the fundamental group of the real projective plane $\mathbb R\mathbb P^2$ minus a point $p$

score 61 · Answer 1 · 2022-08-25 18:02:42

61

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Compute the fundamental group of the real projective plane $\mathbb R\mathbb P^2$ minus a point $p$

Published on 25 Aug 2022 - 18:02

score 106 · Answer 2 · 2022-09-04 17:05:48

106

Views

Show that $\Theta=S^1\cup (\{0\}\times [-1,1])$ is homotopy equivalent to $\infty=(S^1+(1,0))\cup (S^1+(-1,0))$

Published on 04 Sep 2022 - 17:05

score 235 · Answer 3 · 2022-09-04 18:26:30

235

Views

Deformation retraction of Möbius strip minus a point

Published on 04 Sep 2022 - 18:26

score 90 · Answer 4 · 2022-09-08 15:22:27

90

Views

Proving a given circle is not a retract of the Klein bottle -- is my solution correct?

Published on 08 Sep 2022 - 15:22

score 54 · Answer 5 · 2026-02-23 16:57:11

54

Views

Is every splitting-simple group $G$ Hopfian?

Published on 23 Feb 2026 - 16:57

score 253 · Answer 6 · 2022-09-10 15:32:53

253

Views

Does every finitely generated group have finitely many retracts up to isomorphism?

Published on 10 Sep 2022 - 15:32

score 56 · Answer 7 · 2022-09-27 04:42:39

56

Views

Is this homotopy equivalence a deformation retract?

Published on 27 Sep 2022 - 4:42

score 57 · Answer 8 · 2022-10-16 08:38:41

57

Views

Prove or give counter example: $G \cong N \times G/N \Rightarrow N$ has a normal complement.

Published on 16 Oct 2022 - 8:38

score 45 · Answer 9 · 2022-10-20 18:30:44

45

Views

A question related to an induced homomorphism between two groups

Published on 20 Oct 2022 - 18:30

score 185 · Answer 10 · 2022-11-08 19:47:47

185

Views

Proof of Brouwer's fixed point theorem without direct computation

Published on 08 Nov 2022 - 19:47

score 60 · Answer 11 · 2022-12-09 10:57:53

60

Views

Deformation retraction definition – why need the requirement $f_t|A = \mathrm{Id}$ for all $t$?

Published on 09 Dec 2022 - 10:57

score 99 · Answer 12 · 2026-02-23 06:40:32

99

Views

If $(W;\omega)$ is a well-pointed space that weakly contracts onto $\omega$, does it strongly contract onto $\omega$?

Published on 23 Feb 2026 - 6:40

score 103 · Answer 13 · 2022-12-31 18:34:07

103

Views

proving that the inclusions $i:X \to CX$, $j:Y \to C_f$, $j':Y \to M_f$ have the homotopy extension property

Published on 31 Dec 2022 - 18:34

score 47 · Answer 14 · 2023-01-28 07:28:32

Can any compact smooth $n$-dimensional submanifold of the open $n$-ball be deformed into a finite (n-1)-dimensional simplicial complex?

List Question

Compute the fundamental group of the real projective plane $\mathbb R\mathbb P^2$ minus a point $p$

Show that $\Theta=S^1\cup (\{0\}\times [-1,1])$ is homotopy equivalent to $\infty=(S^1+(1,0))\cup (S^1+(-1,0))$

Deformation retraction of Möbius strip minus a point

Proving a given circle is not a retract of the Klein bottle -- is my solution correct?

Is every splitting-simple group $G$ Hopfian?

Does every finitely generated group have finitely many retracts up to isomorphism?

Is this homotopy equivalence a deformation retract?

Prove or give counter example: $G \cong N \times G/N \Rightarrow N$ has a normal complement.

A question related to an induced homomorphism between two groups

Proof of Brouwer's fixed point theorem without direct computation

Deformation retraction definition – why need the requirement $f_t|A = \mathrm{Id}$ for all $t$?

If $(W;\omega)$ is a well-pointed space that weakly contracts onto $\omega$, does it strongly contract onto $\omega$?

proving that the inclusions $i:X \to CX$, $j:Y \to C_f$, $j':Y \to M_f$ have the homotopy extension property

Can any compact smooth $n$-dimensional submanifold of the open $n$-ball be deformed into a finite (n-1)-dimensional simplicial complex?

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