Question

Show that $\mathbb{PR}^1$ is diffeomorphic to $S^1$

score 255 · Answer 1 · 2026-04-28 08:31:31

255

Views

Show that $\mathbb{PR}^1$ is diffeomorphic to $S^1$

Published on 28 Apr 2026 - 8:31

score 63 · Answer 2 · 2026-04-13 16:58:44

63

Views

unique differentiable atlas making $F$ diffeomorphims

Published on 13 Apr 2026 - 16:58

score 1.1k · Answer 3 · 2026-03-30 06:50:04

1.1k

Views

Is it possible to have a connected manifold that is a double cover of a 2-sphere?

Published on 30 Mar 2026 - 6:50

score 129 · Answer 4 · 2026-04-16 19:20:47

129

Views

Two vector bundles over same base manifold $X$

Published on 16 Apr 2026 - 19:20

score 129 · Answer 5 · 2026-03-06 16:00:20

129

Views

Whether there exists some compact manifold whose continuous map must have a fixed point?

Published on 06 Mar 2026 - 16:00

score 106 · Answer 6 · 2026-04-15 09:09:15

106

Views

If $M$ is a manifold, then $\partial(\partial M)) = \emptyset.$

Published on 15 Apr 2026 - 9:09

score 1.1k · Answer 7 · 2026-03-27 07:19:48

1.1k

Views

Calculation of extrinsic curvature

Published on 27 Mar 2026 - 7:19

score 173 · Answer 8 · 2026-04-11 10:22:43

173

Views

How to define CW-complex structure on cubic surface in $CP^3$?

Published on 11 Apr 2026 - 10:22

score 558 · Answer 9 · 2026-04-12 13:37:28

558

Views

Lee, Introduction to Smooth Manifolds, Change of Coordinates

Published on 12 Apr 2026 - 13:37

score 368 · Answer 10 · 2026-04-10 18:47:44

368

Views

How does an almost complex structure on a manifold induce an orientation?

Published on 10 Apr 2026 - 18:47

score 156 · Answer 11 · 2026-04-13 20:05:34

156

Views

Two figures, one is not a manifold, but the other is a manifold, but they look both as suffering from the same deficiencies for not being a manifold

Published on 13 Apr 2026 - 20:05

score 281 · Answer 12 · 2026-04-14 11:36:06

281

Views

signature of the topological manifold $M= \mathbb{C}P^6\times \mathbb{C}P^6$ (using homology, cohomology)

Published on 14 Apr 2026 - 11:36

score 124 · Answer 13 · 2026-04-11 05:15:41

124

Views

A maybe naive question about the definition of manifolds and the common analogy with real-world atlases

Published on 11 Apr 2026 - 5:15

score 61 · Answer 14 · 2026-04-14 13:28:37

61

Views

If $M = \partial W$, with $W$ parallelizable, then an embedding $\iota : M \to S^{n+k}$ extends to an embedding $W \to D^{n+k+1}$

Published on 14 Apr 2026 - 13:28

score 1.1k · Answer 15 · 2026-04-24 03:14:40

1.1k

Views

Cartesian Product of Compact Set and Non-Compact Set is Non-Compact

Published on 24 Apr 2026 - 3:14

List Question

Show that $\mathbb{PR}^1$ is diffeomorphic to $S^1$

unique differentiable atlas making $F$ diffeomorphims

Is it possible to have a connected manifold that is a double cover of a 2-sphere?

Two vector bundles over same base manifold $X$

Whether there exists some compact manifold whose continuous map must have a fixed point?

If $M$ is a manifold, then $\partial(\partial M)) = \emptyset.$

Calculation of extrinsic curvature

How to define CW-complex structure on cubic surface in $CP^3$?

Lee, Introduction to Smooth Manifolds, Change of Coordinates

How does an almost complex structure on a manifold induce an orientation?

Two figures, one is not a manifold, but the other is a manifold, but they look both as suffering from the same deficiencies for not being a manifold

signature of the topological manifold $M= \mathbb{C}P^6\times \mathbb{C}P^6$ (using homology, cohomology)

A maybe naive question about the definition of manifolds and the common analogy with real-world atlases

If $M = \partial W$, with $W$ parallelizable, then an embedding $\iota : M \to S^{n+k}$ extends to an embedding $W \to D^{n+k+1}$

Cartesian Product of Compact Set and Non-Compact Set is Non-Compact

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