List questions from manifolds

Published on 08 Apr 2026 - 0:46

145

Views

Why is the dimension of a homogeneous $G$ space with stabilizer $H$ equal to $\dim G - \dim H$?

Published on 28 Feb 2017 - 16:13

120

Views

Dimension of $X$ as a manifold and as a variety. Are they the same?

Published on 28 Feb 2017 - 16:24

1k

Views

Using the definition of a manifold directly prove that the $2$-sphere $S^2 \subset \mathbb{R}^3$ is a $C^\infty$-manifold of dimension $2$.

Published on 28 Feb 2017 - 17:28

589

Views

Is the complex tangent space closed under conjugation?

Published on 25 Mar 2026 - 17:37

107

Views

mapping class group and system of disks

Published on 01 Apr 2026 - 17:17

2.7k

Views

Prove that the $n-sphere$ is a manifold

Published on 02 Mar 2017 - 16:45

67

Views

Compact, simply connected $C^1$ manifold bounded between two spheres

Published on 02 Mar 2017 - 20:44

1k

Views

Curve in osculating plane if acceleration is constant

Published on 12 Apr 2026 - 0:22

495

Views

Values of $r$ for which $F$ is transverse to $S_r(0)$

Published on 25 Mar 2026 - 11:14

89

Views

Vector structure of $T_pM$ using the derivative of a chart

Published on 02 Mar 2017 - 22:56

1.2k

Views

Integrating a given 2-form over a general Torus

Published on 02 Apr 2026 - 11:57

413

Views

How to prove that the center of the fundamental group of $T_g$ is trivial for $g \geq 2$?

Published on 28 Mar 2026 - 10:29

1k

Views

Every smooth map from $M$ to $\mathbb{R}^N$ can be approximated by smooth immersions

Published on 25 Mar 2026 - 17:37

21

Views

Images of the derivatives of different charts are equal

Published on 04 Mar 2017 - 0:17

List Question

$\omega_{FS}^n$, the top form of Fubini Study metric

Why is the dimension of a homogeneous $G$ space with stabilizer $H$ equal to $\dim G - \dim H$?

Dimension of $X$ as a manifold and as a variety. Are they the same?

Using the definition of a manifold directly prove that the $2$-sphere $S^2 \subset \mathbb{R}^3$ is a $C^\infty$-manifold of dimension $2$.

Is the complex tangent space closed under conjugation?

mapping class group and system of disks

Prove that the $n-sphere$ is a manifold

Compact, simply connected $C^1$ manifold bounded between two spheres

Curve in osculating plane if acceleration is constant

Values of $r$ for which $F$ is transverse to $S_r(0)$

Vector structure of $T_pM$ using the derivative of a chart

Integrating a given 2-form over a general Torus

How to prove that the center of the fundamental group of $T_g$ is trivial for $g \geq 2$?

Every smooth map from $M$ to $\mathbb{R}^N$ can be approximated by smooth immersions

Images of the derivatives of different charts are equal

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