List questions from manifolds

Published on 08 Apr 2026 - 6:43

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Provide an example of a locally Euclidean, paracompact Hausdorff space but not have a countable basis.

Published on 13 Apr 2026 - 8:16

456

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Why aren't two cones attached in their vertex a manifold?

Published on 12 Apr 2026 - 10:43

1.8k

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Two non-equivalent atlas on $\mathbb S^1$

Published on 14 Apr 2026 - 23:42

1k

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Homology of non-orientable manifolds.

Published on 10 Apr 2026 - 22:04

85

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What is the relationship between the Liouvelle measure on $T^1(\mathbb{H})$, and the Haar measure $\mu$ on $PSL(2, \mathbb{R})$?

Published on 11 Apr 2026 - 14:25

881

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Degree of $P$ as a smooth function equals its polynomial degree $d$.

Published on 24 Apr 2026 - 21:54

1k

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Does the zero locus of homogeneous polynomial always form a manifold?

Published on 12 Apr 2026 - 1:39

58

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exactness of product of forms

Published on 13 Apr 2026 - 10:25

25

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Y is $f_t$-related to Y implies $f_t(g_s(p)=g_s(f_t(p))$ for all p$\in M$?

Published on 16 Apr 2026 - 1:47

724

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Struggling to understand real projective space

Published on 11 Apr 2026 - 19:45

904

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Integral of the Laplace-Beltrami Operator multiplied by a function

Published on 07 Apr 2026 - 12:58

97

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Vanishing of index of elliptic operators on odd dimensional manifolds

Published on 12 Apr 2026 - 18:54

760

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Can intersection of two manifolds be $xy=0$

Published on 14 Apr 2026 - 2:32

3.1k

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Tangent vectors as derivatives

Published on 26 Apr 2026 - 7:13

List Question

Two problems about manifolds

Provide an example of a locally Euclidean, paracompact Hausdorff space but not have a countable basis.

Why aren't two cones attached in their vertex a manifold?

Two non-equivalent atlas on $\mathbb S^1$

Homology of non-orientable manifolds.

What is the relationship between the Liouvelle measure on $T^1(\mathbb{H})$, and the Haar measure $\mu$ on $PSL(2, \mathbb{R})$?

Degree of $P$ as a smooth function equals its polynomial degree $d$.

Does the zero locus of homogeneous polynomial always form a manifold?

exactness of product of forms

Y is $f_t$-related to Y implies $f_t(g_s(p)=g_s(f_t(p))$ for all p$\in M$?

Struggling to understand real projective space

Integral of the Laplace-Beltrami Operator multiplied by a function

Vanishing of index of elliptic operators on odd dimensional manifolds

Can intersection of two manifolds be $xy=0$

Tangent vectors as derivatives

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