List questions from differential-topology

Published on 14 Apr 2026 - 11:10

93

Views

2-connected 6 manifolds with boundary $S^5$

Published on 15 Apr 2026 - 13:08

148

Views

Two smoothly homotopic smooth maps induce same maps on de Rham cohomology

Published on 16 Apr 2026 - 10:55

822

Views

Does there exist a $1$-form $\alpha$ with $d\alpha = \omega$?

Published on 08 Apr 2026 - 16:22

207

Views

Two neighborhoods of $0$ in the plane and the upper half plane (resp.) cannot be diffeomorphic.

Published on 12 Apr 2026 - 17:43

70

Views

Smooth representative $f: S^{2n - 1} \to S^n$, do we have $f^*\omega = d\alpha$?

Published on 15 Apr 2026 - 21:47

76

Views

Is $H([f]) = \int_{S^{2n - 1}} \alpha \wedge d\alpha$ independent of all choices, defines a map $H: \pi_{2n - 1}(S^n) \to \mathbb{Z}$?

Published on 17 Apr 2026 - 12:56

457

Views

Topological manifold but not "smooth"

Published on 12 Apr 2026 - 19:43

24

Views

Subvariety in $\mathbb R^n$

Published on 13 Apr 2026 - 21:17

1.1k

Views

Does the set of diffeomorphisms which are induced by flows form a group?

Published on 12 Apr 2026 - 7:48

74

Views

Topology of complex variety $Y^2=F(X)$

Published on 14 Apr 2026 - 0:27

102

Views

The circle does not intersect the unbounded component of $\mathbb{R}^2 \setminus C$

Published on 28 Mar 2026 - 16:20

185

Views

Is range of completely continuous of bounded set finite dimensional set?

Published on 29 Mar 2026 - 7:30

331

Views

Unique way to show $S^n$, $n \geq 2$ is simply connected.

Published on 31 Mar 2026 - 14:28

1.2k

Views

A map of a compact connected manifold with non-empty boundary to a sphere of the same dimension is null-homotopic

Published on 31 Mar 2026 - 3:58

List Question

Wedge product of closed form each with integral periods has integral period?

2-connected 6 manifolds with boundary $S^5$

Two smoothly homotopic smooth maps induce same maps on de Rham cohomology

Does there exist a $1$-form $\alpha$ with $d\alpha = \omega$?

Two neighborhoods of $0$ in the plane and the upper half plane (resp.) cannot be diffeomorphic.

Smooth representative $f: S^{2n - 1} \to S^n$, do we have $f^*\omega = d\alpha$?

Is $H([f]) = \int_{S^{2n - 1}} \alpha \wedge d\alpha$ independent of all choices, defines a map $H: \pi_{2n - 1}(S^n) \to \mathbb{Z}$?

Topological manifold but not "smooth"

Subvariety in $\mathbb R^n$

Does the set of diffeomorphisms which are induced by flows form a group?

Topology of complex variety $Y^2=F(X)$

The circle does not intersect the unbounded component of $\mathbb{R}^2 \setminus C$

Is range of completely continuous of bounded set finite dimensional set?

Unique way to show $S^n$, $n \geq 2$ is simply connected.

A map of a compact connected manifold with non-empty boundary to a sphere of the same dimension is null-homotopic

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