Question

Homology/Cohomology Theories for Non-Locally Connected Spaces

score 330 · Answer 1 · 2026-03-22 22:33:59

330

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Homology/Cohomology Theories for Non-Locally Connected Spaces

Published on 22 Mar 2026 - 22:33

score 847 · Answer 2 · 2026-03-29 23:58:50

847

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Connected, compact, orientable smooth manifold with finite fundamental group

Published on 29 Mar 2026 - 23:58

score 133 · Answer 3 · 2026-03-25 12:41:53

133

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Killing 2nd homology by including 3-manifold as the boundary of a 4-manifold

Published on 25 Mar 2026 - 12:41

score 82 · Answer 4 · 2026-03-29 22:09:18

82

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$f: C_\to D_$ is a homotopy equivalence between chain complexes. Prove that $f_: H_n(C_)\to H_n(D_*)$ is an isomorphism

Published on 29 Mar 2026 - 22:09

score 2.6k · Answer 5 · 2026-03-29 22:13:51

2.6k

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Show that the Euler characteristic of a chain complex is equal to the Euler characteristic of its homology

Published on 29 Mar 2026 - 22:13

score 1k · Answer 6 · 2026-03-29 22:09:16

1k

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Prove that $C_$ is acyclic if and only if the trivial homomorphism $f_: C_\to D_$ is a homotopic equivalence.

Published on 29 Mar 2026 - 22:09

score 647 · Answer 7 · 2026-03-26 23:09:45

647

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Reference for CW-Complexes

Published on 26 Mar 2026 - 23:09

score 115 · Answer 8 · 2018-06-04 23:44:57

115

Views

Show that the barycentric coordinates $t_o(x), t_1(x),...,t_n(x)$ continually depend on $x$.

Published on 04 Jun 2018 - 23:44

score 67 · Answer 9 · 2026-03-30 00:04:11

67

Views

Let $W=[0,1]\times[0,1]$, where $(0,y)\sim(1,1-y)$ for all $0\leq y\leq 1$. Calculate the homology groups of $W$

Published on 30 Mar 2026 - 0:04

score 226 · Answer 10 · 2026-03-30 01:53:07

226

Views

Using Mayer-Vietoris to compute Homology

Published on 30 Mar 2026 - 1:53

score 623 · Answer 11 · 2018-06-05 13:54:18

623

Views

Is there a continuous surjective map of $\mathbb{R}$ onto $\mathbb{R}^{\infty}$?

Published on 05 Jun 2018 - 13:54

score 72 · Answer 12 · 2018-06-05 15:05:52

72

Views

is there any contractable space with three points?

Published on 05 Jun 2018 - 15:05

score 60 · Answer 13 · 2018-06-05 15:53:43

60

Views

Does for every Continuous function $f:S^1 * S^1$ to $\mathbb{R}^2$ exist a point for which $f(a,b)=f(-a,-b)$?

Published on 05 Jun 2018 - 15:53

score 150 · Answer 14 · 2026-03-27 03:58:10

150

Views

The (orbifold) space of symmetric complex matrix

Published on 27 Mar 2026 - 3:58

score 608 · Answer 15 · 2026-03-25 12:49:50

608

Views

There is no 3-dimensional manifold with fundamental group isomorphic to direct sum of four copies of $\Bbb Z$

Published on 25 Mar 2026 - 12:49

List Question

Homology/Cohomology Theories for Non-Locally Connected Spaces

Connected, compact, orientable smooth manifold with finite fundamental group

Killing 2nd homology by including 3-manifold as the boundary of a 4-manifold

$f: C_\to D_$ is a homotopy equivalence between chain complexes. Prove that $f_: H_n(C_)\to H_n(D_*)$ is an isomorphism

Show that the Euler characteristic of a chain complex is equal to the Euler characteristic of its homology

Prove that $C_$ is acyclic if and only if the trivial homomorphism $f_: C_\to D_$ is a homotopic equivalence.

Reference for CW-Complexes

Show that the barycentric coordinates $t_o(x), t_1(x),...,t_n(x)$ continually depend on $x$.

Let $W=[0,1]\times[0,1]$, where $(0,y)\sim(1,1-y)$ for all $0\leq y\leq 1$. Calculate the homology groups of $W$

Using Mayer-Vietoris to compute Homology

Is there a continuous surjective map of $\mathbb{R}$ onto $\mathbb{R}^{\infty}$?

is there any contractable space with three points?

Does for every Continuous function $f:S^1 * S^1$ to $\mathbb{R}^2$ exist a point for which $f(a,b)=f(-a,-b)$?

The (orbifold) space of symmetric complex matrix

There is no 3-dimensional manifold with fundamental group isomorphic to direct sum of four copies of $\Bbb Z$

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