List questions from non-orientable-surfaces

Published on 08 Mar 2026 - 22:17

203

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Is the Poincaré dual of the first Stiefel-Whitney class of a manifold necessarily orientable?

Published on 21 May 2020 - 5:07

848

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I'm looking for a proof for the Euler Characteristic of non-orientable surfaces, $χ=2−k$

Published on 24 May 2020 - 11:52

121

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Rational cohomology of punctured closed non-orientable manifold.

Published on 26 May 2020 - 8:15

30

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Is there a way to compute the orientability of a surface embedded in 3D and represented by a collection of datapoints?

Published on 30 Jun 2020 - 17:49

184

Views

Minimum number of closed simple curves that separates a surface

Published on 26 Feb 2023 - 22:44

133

Views

Orientability and blow-ups

Published on 14 Mar 2023 - 8:57

112

Views

Show that $\mathbb RP^n$ with the standard smooth structure is orientable if and only if $n$ is odd

Published on 25 Apr 2023 - 18:13

446

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Proving $\mathbb{R}P^n$ is orientable if and only if $n$ is odd.

Published on 06 May 2023 - 10:50

192

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Does every surface admit a quadrangulation?

Published on 20 May 2023 - 0:50

73

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Let $M=(\mathbb{S}^2\times [0,1])/\sim$, where $(p,0)\sim (-p, 1)$. Prove that M is a compact, differentiable manifold. Is it orientable?

Published on 12 Jun 2023 - 1:55

33

Views

Orientable surface $M\subset\mathbb{R^{m+n}}$ such that has no normal linearly independent vector fields

Published on 21 Aug 2023 - 19:15

134

Views

Topology of Mobius Strip

Published on 25 Mar 2026 - 16:02

66

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An example of a non hausdorff space

Published on 23 Feb 2026 - 4:55

88

Views

Non-orientable surface in math meme

Published on 03 Feb 2024 - 19:15

List Question

Möbius strips with 3 twists to make a Klein bottle

Is the Poincaré dual of the first Stiefel-Whitney class of a manifold necessarily orientable?

I'm looking for a proof for the Euler Characteristic of non-orientable surfaces, $χ=2−k$

Rational cohomology of punctured closed non-orientable manifold.

Is there a way to compute the orientability of a surface embedded in 3D and represented by a collection of datapoints?

Minimum number of closed simple curves that separates a surface

Orientability and blow-ups

Show that $\mathbb RP^n$ with the standard smooth structure is orientable if and only if $n$ is odd

Proving $\mathbb{R}P^n$ is orientable if and only if $n$ is odd.

Does every surface admit a quadrangulation?

Let $M=(\mathbb{S}^2\times [0,1])/\sim$, where $(p,0)\sim (-p, 1)$. Prove that M is a compact, differentiable manifold. Is it orientable?

Orientable surface $M\subset\mathbb{R^{m+n}}$ such that has no normal linearly independent vector fields

Topology of Mobius Strip

An example of a non hausdorff space

Non-orientable surface in math meme

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