Question

Hatcher exercise 3.2.14 - on the surjectivity of the map $q: \mathbb{R}P^2 \to \mathbb{C}P^1$ in cohomology $H^2$

score 521 · Answer 1 · 2019-12-13 01:36:14

521

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Hatcher exercise 3.2.14 - on the surjectivity of the map $q: \mathbb{R}P^2 \to \mathbb{C}P^1$ in cohomology $H^2$

Published on 13 Dec 2019 - 1:36

score 89 · Answer 2 · 2019-12-20 23:34:13

89

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Degree-wise free chain complexes over $Z$ and CW-complexes

Published on 20 Dec 2019 - 23:34

score 407 · Answer 3 · 2019-12-23 09:13:10

407

Views

Relation between half smash and smash product

Published on 23 Dec 2019 - 9:13

score 100 · Answer 4 · 2019-12-24 23:38:45

100

Views

For $n>>i$ the maps $h^i(X) \to h^i(X^n)$ and $k^i(X) \to k^i(X^n)$ induced by the inclusion $X^n \to X$ are isomorphisms.

Published on 24 Dec 2019 - 23:38

score 54 · Answer 5 · 2019-12-25 17:11:46

54

Views

For CW pairs $(X,A),(Y,B)$, $X\times Y/A\times Y\cup X\times B$ and $X\times (Y/B)/A\times (Y/B)\cup X \times (B/B)$ are homeomorphic

Published on 25 Dec 2019 - 17:11

score 140 · Answer 6 · 2026-03-25 12:46:05

140

Views

Does every closed manifold have a finite CW structure?

Published on 25 Mar 2026 - 12:46

score 699 · Answer 7 · 2020-01-02 03:17:06

699

Views

Cell decomposition for $\mathbb{C}P^n$ that has $\mathbb{R}P^n$ as a subcomplex?

Published on 02 Jan 2020 - 3:17

score 440 · Answer 8 · 2020-01-05 20:24:14

440

Views

Isomorphism of the homology group to the associated cellular homology group

Published on 05 Jan 2020 - 20:24

score 134 · Answer 9 · 2020-01-12 23:59:48

134

Views

Relative Mapping Cylinders

Published on 12 Jan 2020 - 23:59

score 258 · Answer 10 · 2020-01-13 05:31:38

258

Views

Uniqueness of CW approximations

Published on 13 Jan 2020 - 5:31

score 106 · Answer 11 · 2020-01-14 05:11:35

106

Views

A CW complex may have any point as a $0$-cell?

Published on 14 Jan 2020 - 5:11

score 222 · Answer 12 · 2020-01-18 07:53:02

222

Views

Universal cover of a space with cell attached

Published on 18 Jan 2020 - 7:53

score 81 · Answer 13 · 2026-02-23 01:08:25

81

Views

confusion in a proof of local finiteness of partitions of unity in CW complexes in John Lee's Introduction to Smooth Manifolds

Published on 23 Feb 2026 - 1:08

score 107 · Answer 14 · 2020-01-19 21:52:36

107

Views

Whitehead's theorem for maps

Published on 19 Jan 2020 - 21:52

score 447 · Answer 15 · 2020-01-20 02:33:36

447

Views

Hatcher's proof of Quillen plus construction

Published on 20 Jan 2020 - 2:33

List Question

Hatcher exercise 3.2.14 - on the surjectivity of the map $q: \mathbb{R}P^2 \to \mathbb{C}P^1$ in cohomology $H^2$

Degree-wise free chain complexes over $Z$ and CW-complexes

Relation between half smash and smash product

For $n>>i$ the maps $h^i(X) \to h^i(X^n)$ and $k^i(X) \to k^i(X^n)$ induced by the inclusion $X^n \to X$ are isomorphisms.

For CW pairs $(X,A),(Y,B)$, $X\times Y/A\times Y\cup X\times B$ and $X\times (Y/B)/A\times (Y/B)\cup X \times (B/B)$ are homeomorphic

Does every closed manifold have a finite CW structure?

Cell decomposition for $\mathbb{C}P^n$ that has $\mathbb{R}P^n$ as a subcomplex?

Isomorphism of the homology group to the associated cellular homology group

Relative Mapping Cylinders

Uniqueness of CW approximations

A CW complex may have any point as a $0$-cell?

Universal cover of a space with cell attached

confusion in a proof of local finiteness of partitions of unity in CW complexes in John Lee's Introduction to Smooth Manifolds

Whitehead's theorem for maps

Hatcher's proof of Quillen plus construction

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