Question

If $\Sigma$ is a homotopy sphere, then $\Sigma\#(-\Sigma)$ bounds a contractible manifold.

score 149 · Answer 1 · 2026-03-28 18:17:10

149

Views

If $\Sigma$ is a homotopy sphere, then $\Sigma\#(-\Sigma)$ bounds a contractible manifold.

Published on 28 Mar 2026 - 18:17

score 1.6k · Answer 2 · 2018-11-07 01:45:25

1.6k

Views

Nonhomotopic retractions $S^1\vee S^1\to S^1$ without Seifert-Van Kampen?

Published on 07 Nov 2018 - 1:45

score 121 · Answer 3 · 2026-03-25 14:34:42

121

Views

Understanding the definition of the projective sphere and quotient spaces

Published on 25 Mar 2026 - 14:34

score 960 · Answer 4 · 2026-03-25 23:42:46

960

Views

Let $\varphi: G \to G'$ be an injective homomorphism. If $G'$ is Abelian, then $G$ is Abelian? The context is fundamental groups.

Published on 25 Mar 2026 - 23:42

score 1.1k · Answer 5 · 2026-03-31 13:07:14

1.1k

Views

is it true that surjective chain map induce surjective homomorphism between homology groups?

Published on 31 Mar 2026 - 13:07

score 432 · Answer 6 · 2026-03-31 13:17:10

432

Views

Singular cohomology with compact support of $X \times \mathbb{R}$

Published on 31 Mar 2026 - 13:17

score 185 · Answer 7 · 2018-11-08 01:03:40

185

Views

When is commuting in $\pi_1$ equivalent to commuting up to homotopy?

Published on 08 Nov 2018 - 1:03

score 41 · Answer 8 · 2026-03-26 14:43:06

41

Views

Separation from family of closed and connected subsets

Published on 26 Mar 2026 - 14:43

score 1.3k · Answer 9 · 2026-03-25 11:27:17

1.3k

Views

If $A$ and $B$ are isomorphic and $C$ and $D$ are isomorphic, then $A\times C$ and $B\times D$ are isomorphic?

Published on 25 Mar 2026 - 11:27

score 231 · Answer 10 · 2026-03-25 14:25:34

231

Views

Can $G/2G$ and $\mathbb Z / 2\mathbb Z \times ... \times \mathbb Z / 2\mathbb Z$ be not isomorphic? $G$ is a free abelian group with finite basis.

Published on 25 Mar 2026 - 14:25

score 76 · Answer 11 · 2018-11-08 14:14:04

76

Views

$f_n \to f$ then $\tilde{f_n}\to \tilde{f}$ where $\tilde{f_n}$ and $\tilde{f}$ are the lifting of $f_n$ and $f$.

Published on 08 Nov 2018 - 14:14

score 543 · Answer 12 · 2018-11-08 15:16:22

543

Views

Induced map between homology $H_n(S^n) \to H_n(\mathbb RP^n)$

Published on 08 Nov 2018 - 15:16

score 55 · Answer 13 · 2026-03-31 13:06:47

55

Views

A question about universal coefficient theorem

Published on 31 Mar 2026 - 13:06

score 42 · Answer 14 · 2018-11-08 20:39:57

42

Views

Is connectedness needed in this statement?

Published on 08 Nov 2018 - 20:39

score 159 · Answer 15 · 2026-03-31 13:10:23

159

Views

Showing that the sum of any 1-cycle and its opposite orientation is a 1-boundary

Published on 31 Mar 2026 - 13:10

List Question

If $\Sigma$ is a homotopy sphere, then $\Sigma\#(-\Sigma)$ bounds a contractible manifold.

Nonhomotopic retractions $S^1\vee S^1\to S^1$ without Seifert-Van Kampen?

Understanding the definition of the projective sphere and quotient spaces

Let $\varphi: G \to G'$ be an injective homomorphism. If $G'$ is Abelian, then $G$ is Abelian? The context is fundamental groups.

is it true that surjective chain map induce surjective homomorphism between homology groups?

Singular cohomology with compact support of $X \times \mathbb{R}$

When is commuting in $\pi_1$ equivalent to commuting up to homotopy?

Separation from family of closed and connected subsets

If $A$ and $B$ are isomorphic and $C$ and $D$ are isomorphic, then $A\times C$ and $B\times D$ are isomorphic?

Can $G/2G$ and $\mathbb Z / 2\mathbb Z \times ... \times \mathbb Z / 2\mathbb Z$ be not isomorphic? $G$ is a free abelian group with finite basis.

$f_n \to f$ then $\tilde{f_n}\to \tilde{f}$ where $\tilde{f_n}$ and $\tilde{f}$ are the lifting of $f_n$ and $f$.

Induced map between homology $H_n(S^n) \to H_n(\mathbb RP^n)$

A question about universal coefficient theorem

Is connectedness needed in this statement?

Showing that the sum of any 1-cycle and its opposite orientation is a 1-boundary

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