Question

Showing an element of $\pi_n(S^n)$ is a sum of maps acting locally, invertibly near one point

score 42 · Answer 1 · 2021-10-20 14:35:09

42

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Showing an element of $\pi_n(S^n)$ is a sum of maps acting locally, invertibly near one point

Published on 20 Oct 2021 - 14:35

score 238 · Answer 2 · 2021-11-08 07:26:54

238

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If higher homotopy groups are trivial, then the fundamental group is a complete invariant?

Published on 08 Nov 2021 - 7:26

score 271 · Answer 3 · 2021-11-08 13:39:11

271

Views

Definition of weak homotopy equivalence

Published on 08 Nov 2021 - 13:39

score 53 · Answer 4 · 2021-11-10 21:12:54

53

Views

Why does the contractibility of $CX$ imply that $\pi_n(CX,X,x_0)\cong\pi_{n-1}(X,x_0)$?

Published on 10 Nov 2021 - 21:12

score 291 · Answer 5 · 2021-11-11 15:55:13

291

Views

Long exact sequence of homotopy group

Published on 11 Nov 2021 - 15:55

score 294 · Answer 6 · 2021-11-17 19:56:01

294

Views

Does there exist a smooth compact manifold whose homotopy groups are not finitely generated?

Published on 17 Nov 2021 - 19:56

score 311 · Answer 7 · 2021-11-18 09:29:41

311

Views

Action of $\pi_1(\Bbb RP^n)$ on $\pi_n(\Bbb RP^n)$

Published on 18 Nov 2021 - 9:29

score 415 · Answer 8 · 2021-11-18 13:01:00

415

Views

A map between connected $n$-dimensional CW complexes is a homotopy equivalence

Published on 18 Nov 2021 - 13:01

score 242 · Answer 9 · 2021-11-29 22:49:40

242

Views

What is $\pi_3(S^2\times S^1)$?

Published on 29 Nov 2021 - 22:49

score 175 · Answer 10 · 2021-12-13 19:24:45

175

Views

Homotopy group of pairs: equivalent descriptions

Published on 13 Dec 2021 - 19:24

score 113 · Answer 11 · 2022-01-07 21:08:35

113

Views

Why is this CW complex connected?

Published on 07 Jan 2022 - 21:08

score 128 · Answer 12 · 2022-01-09 02:13:45

128

Views

If we have a weak homotopy equivalence $f:X \rightarrow Y$, does there necessarily exist a weak homotopy equivalence $g:Y \rightarrow X$?

Published on 09 Jan 2022 - 2:13

score 67 · Answer 13 · 2022-01-19 19:27:34

67

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Explicit description of $\pi_1(M)$-action on the relative homotopy groups $\pi_k(\Omega_0M,M)$

Published on 19 Jan 2022 - 19:27

score 150 · Answer 14 · 2022-01-26 16:35:17

150

Views

A pair $(X,A)$ is $n$-connected iff the inclusion $A\rightarrow X$ is an $n$-equivalence.

Published on 26 Jan 2022 - 16:35

score 146 · Answer 15 · 2022-02-02 13:58:52

146

Views

Homotopy Lifting Property in Hatcher's Spectral Sequences

Published on 02 Feb 2022 - 13:58

List Question

Showing an element of $\pi_n(S^n)$ is a sum of maps acting locally, invertibly near one point

If higher homotopy groups are trivial, then the fundamental group is a complete invariant?

Definition of weak homotopy equivalence

Why does the contractibility of $CX$ imply that $\pi_n(CX,X,x_0)\cong\pi_{n-1}(X,x_0)$?

Long exact sequence of homotopy group

Does there exist a smooth compact manifold whose homotopy groups are not finitely generated?

Action of $\pi_1(\Bbb RP^n)$ on $\pi_n(\Bbb RP^n)$

A map between connected $n$-dimensional CW complexes is a homotopy equivalence

What is $\pi_3(S^2\times S^1)$?

Homotopy group of pairs: equivalent descriptions

Why is this CW complex connected?

If we have a weak homotopy equivalence $f:X \rightarrow Y$, does there necessarily exist a weak homotopy equivalence $g:Y \rightarrow X$?

Explicit description of $\pi_1(M)$-action on the relative homotopy groups $\pi_k(\Omega_0M,M)$

A pair $(X,A)$ is $n$-connected iff the inclusion $A\rightarrow X$ is an $n$-equivalence.

Homotopy Lifting Property in Hatcher's Spectral Sequences

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