Questions tagged [mobius-band]

The Möbius band or Möbius strip is a surface with only one side and only one boundary. The Möbius strip has the mathematical property of being non-orientable. It is named after the German mathematician August Ferdinand Möbius.

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Knots on $\mathbb{R}P^2$ and on n-half-twist Möbius strips

Can you embed a non-trivial knot on the surface of $\mathbb{R}P^2$? I know we can on a torus, and we can't on a 2-sphere. My hand-wavy argument/intuition based on the little I know from self study of ...
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When is an open subset of an orientable manifold an orientable submanifold?

I am trying to complete problem $4$ from the introductory chapter of Riemannian Geometry by do Carmo. The question asks us to show that the projective plane $P^2(\mathbb{R})$ is non-orientable, first ...
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Moebius strip orientability

Let $\{M\}$ be the one-sided Moebius strip and $\{MM\}$ the corresponding two-sheeted Moebius strip. Let us assume $\{MM\}$ to be the doubling of $\{M\}$; hence it is orientable. Then, $\{M\}$ is ...
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Write two vector bundles of $S^1$, not diffeomorphic between them

I just want your opinion on this one: "1. Write two vector bundles with rank 1 on $S^1$, such that they are not isomorphic between them". "2. Prove that $S^1\times S^1$ is parallelizable For ...
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Tautological vector bundle over G1(R2) isomorphic to the Möbius bundle explicitily?

TShow that the tautological vector bundle over G1(R2) is smoothly isomorphic to the Möbius bundle. How can I write a isomorphism explicitily?
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Cutting a multiple twisted Möbius strip in half

At my workplace in the weekends we ususally play around with science and younger children. This months topic in mathemathics was a bit of soft topology. We of course made Möbius strips. What we called ...
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Möbius Strip is no orientable

This is an exercise from Do Carmo's Riemannian Geometry book. Let $G=\{Id,A\}$, $C= \{ (x, y, z) \in \mathbb{R}^3; x^2 + y^2 = 1, -1 < z < 1 \}$, where $A(p)=-p$. Define $\frac{C}{G}$ the ...
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Does this method determine if we are living in a Mobius strip or cylinder?

Inspired by this question. Suppose we are living on a two-dimensional walkway with railings. Gravity is always directed towards the surface. We know the walkway is either a cylinder or a Mobius strip....
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Is it possible to determine if you were on a Möbius strip?

I understand that if you were to walk on the surface of a Möbius strip you would have the same perspective as if you walked on the outer surface of a cylinder. However, would it be possible for ...
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graph on mobius strip is nonplanar? [duplicate]

Consider the closed curve on the mobius strip that covers both sides of the fundamental polygon: https://thumb9.shutterstock.com/display_pic_with_logo/1663882/462955276/stock-vector-blue-moebius-strip-...