List questions from differential-topology

Published on 06 Nov 2018 - 23:50

148

Views

If $\Sigma$ is a homotopy sphere, then $\Sigma\#(-\Sigma)$ bounds a contractible manifold.

Published on 07 Nov 2018 - 0:12

78

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Show that $G_E=\mathbb{S}^1\times \mathbb{S}^1$

Published on 25 Mar 2026 - 9:23

134

Views

Showing a subset is a submanifold of $T^2$

Published on 07 Nov 2018 - 18:15

391

Views

How to show that $SO(3)$ and $\mathbb{R}P^3$ are diffeomorphic?

Published on 25 Mar 2026 - 6:03

94

Views

A question on topology

Published on 09 Nov 2018 - 18:43

179

Views

Prove that $f$ is Morse function if an only if $det(H)^2 + \sum_{i=1}^k (\frac {\partial f}{\partial x_i})^2>0$(2)

Published on 26 Mar 2026 - 11:17

443

Views

Path components of space of almost complex structures

Published on 26 Mar 2026 - 21:03

41

Views

can a basis for the tangent space of a manifold be found without any use of charts?

Published on 10 Nov 2018 - 18:21

313

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Leray Hirsch from Bott & Tu

Published on 10 Nov 2018 - 23:24

256

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A difficulty in understanding the solution of problem 1.7.17 in Guillemin and Pollack.(p.47)

Published on 25 Mar 2026 - 6:12

171

Views

Bott and Tu, Thom Class pg 64

Published on 11 Nov 2018 - 23:06

84

Views

Showing product of two transversal maps is a transversal

Published on 25 Mar 2026 - 1:31

274

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How is the differential of a Sobolev function on a manifold regarded as an a.e. defined section of $T^*M$?

Published on 25 Mar 2026 - 11:23

44

Views

Integration of the sphere

Published on 27 Mar 2026 - 16:52

List Question

On a proof about rational functions and connected components

If $\Sigma$ is a homotopy sphere, then $\Sigma\#(-\Sigma)$ bounds a contractible manifold.

Show that $G_E=\mathbb{S}^1\times \mathbb{S}^1$

Showing a subset is a submanifold of $T^2$

How to show that $SO(3)$ and $\mathbb{R}P^3$ are diffeomorphic?

A question on topology

Prove that $f$ is Morse function if an only if $det(H)^2 + \sum_{i=1}^k (\frac {\partial f}{\partial x_i})^2>0$(2)

Path components of space of almost complex structures

can a basis for the tangent space of a manifold be found without any use of charts?

Leray Hirsch from Bott & Tu

A difficulty in understanding the solution of problem 1.7.17 in Guillemin and Pollack.(p.47)

Bott and Tu, Thom Class pg 64

Showing product of two transversal maps is a transversal

How is the differential of a Sobolev function on a manifold regarded as an a.e. defined section of $T^*M$?

Integration of the sphere

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