List questions from differential-topology

803

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Let C be an oriented plane curve with curvature k>0. Assume that C has at least one point p of self intersection, prove the following questions:

Published on 12 Apr 2026 - 22:44

641

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Subdifferential of a convex function

Published on 10 Apr 2026 - 10:21

745

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The identity map on a tangent space

Published on 11 Apr 2026 - 21:04

146

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Coordinates at a singularity

Published on 11 Apr 2026 - 14:17

229

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Polynomials of a fixed degree have a nonzero partial at all points of their vanishing set?

Published on 13 Apr 2026 - 7:55

102

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Question on tangent spaces

Published on 11 Apr 2026 - 10:42

100

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principal bundle and the associated bundle

Published on 13 Apr 2026 - 23:05

519

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triviality of tensor product of vector bundles

Published on 16 Apr 2026 - 12:01

670

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What's the "easiest" closed 3-manifold with a nonabelian fundamental group?

Published on 13 Apr 2026 - 12:04

142

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What is the derivative of the map $\mathbb{R}^\ell\times S\to\mathbb{R}^N$ given by $(t_1,\dots,t_\ell,v_1,\dots,v_\ell)\mapsto \sum t_iv_i$?

Published on 15 Apr 2026 - 12:55

431

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Pullbacks of smooth densities through smooth functions are smooth?

Published on 10 Apr 2026 - 22:44

283

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Framing of embedding induces an isotopy of embeddings

Published on 12 Apr 2026 - 6:10

212

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A(nother ignorant) question on phantom maps

Published on 13 Apr 2026 - 6:08

559

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If $f\colon X\to Y$ is nullhomotopic, then $I_2(f,Z)=0$ for closed $Z\subset Y$ of complementary dimension?

Published on 15 Apr 2026 - 7:25

123

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Local bisections of Lie groupoids

Published on 25 Mar 2026 - 6:04

List Question

Let C be an oriented plane curve with curvature k>0. Assume that C has at least one point p of self intersection, prove the following questions:

Subdifferential of a convex function

The identity map on a tangent space

Coordinates at a singularity

Polynomials of a fixed degree have a nonzero partial at all points of their vanishing set?

Question on tangent spaces

principal bundle and the associated bundle

triviality of tensor product of vector bundles

What's the "easiest" closed 3-manifold with a nonabelian fundamental group?

What is the derivative of the map $\mathbb{R}^\ell\times S\to\mathbb{R}^N$ given by $(t_1,\dots,t_\ell,v_1,\dots,v_\ell)\mapsto \sum t_iv_i$?

Pullbacks of smooth densities through smooth functions are smooth?

Framing of embedding induces an isotopy of embeddings

A(nother ignorant) question on phantom maps

If $f\colon X\to Y$ is nullhomotopic, then $I_2(f,Z)=0$ for closed $Z\subset Y$ of complementary dimension?

Local bisections of Lie groupoids

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