List questions from manifolds

Published on 13 Apr 2026 - 22:12

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Can we recover a compact smooth manifold from its ring of smooth functions?

Published on 28 Apr 2026 - 16:51

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Prove the boundary is a compact 1 manifold

Published on 15 Apr 2026 - 5:34

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What can you say about the $k$-th cohomology group of a closed orientable $n$-manifold for $k = n$ and $k = n-1$?

Published on 14 Apr 2026 - 22:13

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What is concretely a vector field?

Published on 13 Apr 2026 - 10:44

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Counterexample for the density of smooth functions in Sobolev spaces on a manifold

Published on 17 Apr 2026 - 22:37

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Specific example of integrating a 1-form over a curve

Published on 14 Apr 2026 - 10:36

119

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Why is $\int_{X} d(\alpha \wedge *\bar{\beta})$ zero on a compact hermitian manifold?

Published on 28 Mar 2026 - 1:48

69

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analysis on manifods

Published on 24 Apr 2026 - 16:53

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Find a nontrivial bundle of $S^1$ with fibre isomorphic to $\mathbb{R}^n$

Published on 16 Apr 2026 - 8:26

860

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How transversality condition implies that a value is regular?

Published on 14 Apr 2026 - 9:09

67

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Integration on k-1 form

Published on 12 Apr 2026 - 7:56

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Oriented atlas on a circle

Published on 27 Mar 2026 - 8:49

806

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Explicit form of the exponential map

Published on 03 May 2026 - 7:42

81

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Prove that integration of a differential $k$-form is independent of choice of basis

Published on 28 Apr 2026 - 18:06

List Question

Examples of Manifolds such that $\chi (X)=-3$

Can we recover a compact smooth manifold from its ring of smooth functions?

Prove the boundary is a compact 1 manifold

What can you say about the $k$-th cohomology group of a closed orientable $n$-manifold for $k = n$ and $k = n-1$?

What is concretely a vector field?

Counterexample for the density of smooth functions in Sobolev spaces on a manifold

Specific example of integrating a 1-form over a curve

Why is $\int_{X} d(\alpha \wedge *\bar{\beta})$ zero on a compact hermitian manifold?

analysis on manifods

Find a nontrivial bundle of $S^1$ with fibre isomorphic to $\mathbb{R}^n$

How transversality condition implies that a value is regular?

Integration on k-1 form

Oriented atlas on a circle

Explicit form of the exponential map

Prove that integration of a differential $k$-form is independent of choice of basis

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