List questions from differential-topology

Published on 14 Apr 2026 - 5:01

32

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Let $X \subseteq \mathbb{R}^{N}$ and $f: X \rightarrow \mathbb{R}^{n}$ be smooth. Then $f$ is continuous w.r.t. the subspace topology $\tau_X$ of $X$

Published on 16 Apr 2026 - 14:53

98

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Classification of Symmetric Spaces of Dimension $n$ and Rank $k$?

Published on 15 May 2026 - 21:54

50

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Homotopy of parts of surface (?)

Published on 15 Apr 2026 - 6:51

80

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Theta characteristic and spin structures

Published on 16 May 2026 - 8:21

40

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$L$ is submanifold of $\mathbb{R}^n$ with $\dim L\leq n-2$.

Published on 11 May 2026 - 9:07

163

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Intersection of lines with submanifold

Published on 11 May 2026 - 8:52

82

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How do we obtain a chart for the sphere $\{x:\|x\|=1\}$ from a chart of the ball $\{x:\|x|\le1\}$?

Published on 15 Apr 2026 - 14:25

171

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$S^1$-valued function on $T^n$

Published on 26 Apr 2026 - 8:33

60

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$q$ is a regular value of $f^\circ=f\mid_{M^\circ}$ or $\partial M$, but $S=f^{-1}(q)$ is not a manifold;

Published on 16 Apr 2026 - 16:20

201

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Different definitions of the Hopf Invariant

Published on 09 Apr 2026 - 20:27

58

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Finding a Retraction for a Collar Neighborhood

Published on 11 Apr 2026 - 12:53

85

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Consequences of the Globalization Theorem in Hirsch's Differential Topology

Published on 15 Apr 2026 - 3:20

169

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Minimum number of charts in atlas

Published on 15 Apr 2026 - 14:33

212

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A satisfying definition of quotient bundles

Published on 11 Apr 2026 - 18:52

List Question

When is a complex surface not symplectic

Let $X \subseteq \mathbb{R}^{N}$ and $f: X \rightarrow \mathbb{R}^{n}$ be smooth. Then $f$ is continuous w.r.t. the subspace topology $\tau_X$ of $X$

Classification of Symmetric Spaces of Dimension $n$ and Rank $k$?

Homotopy of parts of surface (?)

Theta characteristic and spin structures

$L$ is submanifold of $\mathbb{R}^n$ with $\dim L\leq n-2$.

Intersection of lines with submanifold

How do we obtain a chart for the sphere $\{x:\|x\|=1\}$ from a chart of the ball $\{x:\|x|\le1\}$?

$S^1$-valued function on $T^n$

$q$ is a regular value of $f^\circ=f\mid_{M^\circ}$ or $\partial M$, but $S=f^{-1}(q)$ is not a manifold;

Different definitions of the Hopf Invariant

Finding a Retraction for a Collar Neighborhood

Consequences of the Globalization Theorem in Hirsch's Differential Topology

Minimum number of charts in atlas

A satisfying definition of quotient bundles

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