List questions from differential-topology

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Averaging differential forms

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Prerequisites for studying smooth manifold theory?

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Confusion on Cech cohomology

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How to calculate the degree of this Gauss map?

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Why is there no foliations of the 2-sphere, or a genus two surface?

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Transform flat surface into paraboloid

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Geometric meaning of a nondegenerate critical point

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Every $1$-manifold is orientable

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Strong deformation retraction $\mathbb{I}\!\times\!\mathbb{B}^l \longrightarrow \{1\}\!\times\!\mathbb{B}^l\cup \mathbb{I}\!\times\!\{0\}$?

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Showing a certain form is exact

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Manifold/Topology Notation

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A star shaped open set in $\mathbb{R}^n$ is diffeomorphic to $\mathbb{R}^n$

Published on 16 Apr 2026 - 13:04

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If $f\!: X\simeq Y$, then $X\!\cup_\varphi\!\mathbb{B}^k \simeq Y\!\cup_{f\circ\varphi}\!\mathbb{B}^k$.

Published on 15 Apr 2026 - 18:50

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Are close maps homotopic?

Published on 11 Apr 2026 - 12:04

List Question

Retracts are Submanifolds

Averaging differential forms

Prerequisites for studying smooth manifold theory?

Confusion on Cech cohomology

How to calculate the degree of this Gauss map?

Why is there no foliations of the 2-sphere, or a genus two surface?

Transform flat surface into paraboloid

Geometric meaning of a nondegenerate critical point

Every $1$-manifold is orientable

Strong deformation retraction $\mathbb{I}\!\times\!\mathbb{B}^l \longrightarrow \{1\}\!\times\!\mathbb{B}^l\cup \mathbb{I}\!\times\!\{0\}$?

Showing a certain form is exact

Manifold/Topology Notation

A star shaped open set in $\mathbb{R}^n$ is diffeomorphic to $\mathbb{R}^n$

If $f\!: X\simeq Y$, then $X\!\cup_\varphi\!\mathbb{B}^k \simeq Y\!\cup_{f\circ\varphi}\!\mathbb{B}^k$.

Are close maps homotopic?

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