Question

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

score 78 · Answer 1 · 2026-02-23 08:42:02

78

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 23 Feb 2026 - 8:42

score 45 · Answer 2 · 2026-02-23 08:42:05

45

Views

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

Published on 23 Feb 2026 - 8:42

score 178 · Answer 3 · 2026-02-23 08:42:19

178

Views

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

Published on 23 Feb 2026 - 8:42

score 187 · Answer 4 · 2026-02-23 08:36:46

187

Views

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

Published on 23 Feb 2026 - 8:36

score 48 · Answer 5 · 2026-02-23 08:41:13

48

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 23 Feb 2026 - 8:41

score 95 · Answer 6 · 2026-02-23 08:40:55

95

Views

Prove that two quotients of a bounded cylinder are not homeomorphic

Published on 23 Feb 2026 - 8:40

score 182 · Answer 7 · 2026-02-23 08:43:03

182

Views

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

Published on 23 Feb 2026 - 8:43

score 70 · Answer 8 · 2026-02-23 08:41:33

70

Views

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

Published on 23 Feb 2026 - 8:41

score 152 · Answer 9 · 2026-02-23 08:42:19

152

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 23 Feb 2026 - 8:42

score 310 · Answer 10 · 2026-02-23 08:34:57

310

Views

A retract in normal space

Published on 23 Feb 2026 - 8:34

score 390 · Answer 11 · 2026-02-23 08:37:55

390

Views

Retracts of CW-complexes

Published on 23 Feb 2026 - 8:37

score 119 · Answer 12 · 2026-02-23 08:41:14

119

Views

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

Published on 23 Feb 2026 - 8:41

score 261 · Answer 13 · 2026-02-23 08:42:20

261

Views

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

Published on 23 Feb 2026 - 8:42

score 95 · Answer 14 · 2026-02-23 08:38:32

95

Views

Homotopy equivalence iff weak deformation retract

Published on 23 Feb 2026 - 8:38

score 82 · Answer 15 · 2026-02-23 08:36:56

82

Views

Contractible and deformation retract

Published on 23 Feb 2026 - 8:36

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

Trending Questions

Popular # Hahtags

Popular Questions