Question

Does every simply-connected open subset of $S^2$ have connected complement?

score 72 · Answer 1 · 2026-04-12 06:41:36

72

Views

Does every simply-connected open subset of $S^2$ have connected complement?

Published on 12 Apr 2026 - 6:41

score 63 · Answer 2 · 2026-04-11 23:54:52

63

Views

Differentiation in Several Variables

Published on 11 Apr 2026 - 23:54

score 81 · Answer 3 · 2026-03-25 14:29:58

81

Views

A connected compact manifold has a unique orientable line bundle on it

Published on 25 Mar 2026 - 14:29

score 126 · Answer 4 · 2026-03-26 01:34:55

126

Views

Using Laudenbach-Poénaru to justify Kirby diagrams

Published on 26 Mar 2026 - 1:34

score 71 · Answer 5 · 2026-04-11 18:13:13

71

Views

Can the notion of tangent space be recovered from an orthogonal projection?

Published on 11 Apr 2026 - 18:13

score 63 · Answer 6 · 2026-04-12 01:25:27

63

Views

Terminology "Invariance of the Boundary"

Published on 12 Apr 2026 - 1:25

score 173 · Answer 7 · 2023-02-01 09:46:06

173

Views

Proving $\dim\{B\in {\rm M}(n,\mathbb{R}):BA^T=-AB^T\}=\frac{n(n-1)}{2}$ where $A\in {\rm O}(n)$

Published on 01 Feb 2023 - 9:46

score 192 · Answer 8 · 2026-03-30 02:12:08

192

Views

Prove that every manifold is paracompact

Published on 30 Mar 2026 - 2:12

score 53 · Answer 9 · 2026-04-11 08:15:51

53

Views

What is the definition of a diffeomorphism of an abstract smooth surface?

Published on 11 Apr 2026 - 8:15

score 265 · Answer 10 · 2026-03-30 02:06:35

265

Views

Check proof that every manifold has a basis of precompact open sets.

Published on 30 Mar 2026 - 2:06

score 57 · Answer 11 · 2023-02-02 17:25:46

57

Views

trouble with proving/disproving $\lvert z-x \rvert$=$\sqrt{x+y^2}$ is manifold

Published on 02 Feb 2023 - 17:25

score 118 · Answer 12 · 2026-03-26 14:20:30

118

Views

Proving Invariance of CW Complex Dimension

Published on 26 Mar 2026 - 14:20

score 36 · Answer 13 · 2026-03-28 02:04:50

36

Views

Maximize $\log\det(\mathbf{I} + \sum_{i=1}^K \mathbf{H}_i \mathbf{WW}^\top \mathbf{H}_i^\top)$ wrt $\mathbf{W}$ over hypersphere manifold

Published on 28 Mar 2026 - 2:04

score 29 · Answer 14 · 2026-04-12 04:06:41

29

Views

Matrices $2\times 2$ surfaces of codimension 2.

Published on 12 Apr 2026 - 4:06

score 35 · Answer 15 · 2026-04-11 06:11:33

35

Views

Why does it suffice to consider only increasing indices to define the basis of $\Lambda^k(T^*_pU)$?

Published on 11 Apr 2026 - 6:11

List Question

Does every simply-connected open subset of $S^2$ have connected complement?

Differentiation in Several Variables

A connected compact manifold has a unique orientable line bundle on it

Using Laudenbach-Poénaru to justify Kirby diagrams

Can the notion of tangent space be recovered from an orthogonal projection?

Terminology "Invariance of the Boundary"

Proving $\dim\{B\in {\rm M}(n,\mathbb{R}):BA^T=-AB^T\}=\frac{n(n-1)}{2}$ where $A\in {\rm O}(n)$

Prove that every manifold is paracompact

What is the definition of a diffeomorphism of an abstract smooth surface?

Check proof that every manifold has a basis of precompact open sets.

trouble with proving/disproving $\lvert z-x \rvert$=$\sqrt{x+y^2}$ is manifold

Proving Invariance of CW Complex Dimension

Maximize $\log\det(\mathbf{I} + \sum_{i=1}^K \mathbf{H}_i \mathbf{WW}^\top \mathbf{H}_i^\top)$ wrt $\mathbf{W}$ over hypersphere manifold

Matrices $2\times 2$ surfaces of codimension 2.

Why does it suffice to consider only increasing indices to define the basis of $\Lambda^k(T^*_pU)$?

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