Question

Does a deformation retraction of $X$ onto a subspace $A\subset X$ induce an isomorphism $\pi_n(X) \to \pi_n(A)$?

score 77 · Answer 1 · 2020-06-05 02:52:27

77

Views

Does a deformation retraction of $X$ onto a subspace $A\subset X$ induce an isomorphism $\pi_n(X) \to \pi_n(A)$?

Published on 05 Jun 2020 - 2:52

score 44 · Answer 2 · 2020-06-11 20:25:15

44

Views

understanding a statement in the proof of a retract of a contractible space is contractible.

Published on 11 Jun 2020 - 20:25

score 177 · Answer 3 · 2020-06-16 12:58:52

177

Views

Hatcher Theorem 2.13 - is the subspace $X$ of its cone $CX$ a deformation retract of some neighborhood in $CX$?

Published on 16 Jun 2020 - 12:58

score 186 · Answer 4 · 2020-06-23 14:25:07

186

Views

Is $\mathbb{D} = [-1,1]^3$ a compact manifold?

Published on 23 Jun 2020 - 14:25

score 47 · Answer 5 · 2020-07-04 14:14:48

47

Views

prove that $i_{*} :\ \Pi_{1}(A, a) \rightarrow \Pi_{1}(X, a)$ induced a isomorphism while X has a deformation retraction to A.

Published on 04 Jul 2020 - 14:14

score 94 · Answer 6 · 2016-07-30 16:48:39

94

Views

Prove that two quotients of a bounded cylinder are not homeomorphic

Published on 30 Jul 2016 - 16:48

score 181 · Answer 7 · 2016-09-14 20:21:05

181

Views

Retract of $D^n \times [0,1] \times [0,1]$

Published on 14 Sep 2016 - 20:21

score 69 · Answer 8 · 2016-12-25 05:00:37

69

Views

Concerning a retraction $r : X\times I \to X\times \{0\} \cup A\times I$

Published on 25 Dec 2016 - 5:00

score 151 · Answer 9 · 2017-01-14 21:01:26

151

Views

If $A$ is a retract of $X$ (via $r:X\to A$), then $H_q(X)\cong \text{im }i_\oplus \ker r_$

Published on 14 Jan 2017 - 21:01

score 309 · Answer 10 · 2017-02-04 17:44:59

309

Views

A retract in normal space

Published on 04 Feb 2017 - 17:44

score 389 · Answer 11 · 2017-02-06 13:57:24

389

Views

Retracts of CW-complexes

Published on 06 Feb 2017 - 13:57

score 118 · Answer 12 · 2017-02-14 11:09:58

118

Views

Is the intersection of a descending chain of group retracts a retract?

Published on 14 Feb 2017 - 11:09

score 260 · Answer 13 · 2017-04-05 17:13:20

260

Views

Prove: If $n \ge 0$, then $S^n$ is not a retract of $D^{n+1}$ using homology functors.

Published on 05 Apr 2017 - 17:13

score 94 · Answer 14 · 2023-02-05 10:38:32

94

Views

Homotopy equivalence iff weak deformation retract

Published on 05 Feb 2023 - 10:38

score 81 · Answer 15 · 2023-03-06 15:27:46

81

Views

Contractible and deformation retract

Published on 06 Mar 2023 - 15:27

List Question

Does a deformation retraction of $X$ onto a subspace $A\subset X$ induce an isomorphism $\pi_n(X) \to \pi_n(A)$?

understanding a statement in the proof of a retract of a contractible space is contractible.

Hatcher Theorem 2.13 - is the subspace $X$ of its cone $CX$ a deformation retract of some neighborhood in $CX$?

Is $\mathbb{D} = [-1,1]^3$ a compact manifold?

prove that $i_{*} :\ \Pi_{1}(A, a) \rightarrow \Pi_{1}(X, a)$ induced a isomorphism while X has a deformation retraction to A.

Prove that two quotients of a bounded cylinder are not homeomorphic

Retract of $D^n \times [0,1] \times [0,1]$

Concerning a retraction $r : X\times I \to X\times \{0\} \cup A\times I$

If $A$ is a retract of $X$ (via $r:X\to A$), then $H_q(X)\cong \text{im }i_\oplus \ker r_$

A retract in normal space

Retracts of CW-complexes

Is the intersection of a descending chain of group retracts a retract?

Prove: If $n \ge 0$, then $S^n$ is not a retract of $D^{n+1}$ using homology functors.

Homotopy equivalence iff weak deformation retract

Contractible and deformation retract

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