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Questions tagged [non-orientable-surfaces]

For all questions about Möbius bands, Klein bottles, projective planes or surfaces built from these (via surgeries, gluings...), intersection or boundary problems, embeddings...

3
votes
1answer
731 views

Torus/Möbius Band homeomorphism

Is a fattened Möbius Spiral Band homeomorphic to a Torus? (Due to the same Euler Characteristic $\chi$ ?) Are both non-orientable? Following (3D printable plastic) Torus has a square section that ...
7
votes
1answer
291 views

Fixed points in mapping from Möbius strip to disk [Explanation or reference needed]

One of the most elegant demonstrations in topology is the proof of the inscribed rectangle problem (a solved variant of the unsolved inscribed square problem) which states that for any plain, closed ...
3
votes
1answer
69 views

When you divide the real projective plane into two subsets, does it always have exactly one non-orientable component?

Let's say you divide the real projective plane into two subsets, are exactly one these subsets non-orientable? In particular, we will require that each subset $S$ is "nice" in the sense their common ...
2
votes
1answer
832 views

Orientable Surface Covers Non-Orientable Surface

I need to describe how a 4-genus orientable surface double covers a genus 5-non-orientable surface. I know that in general every non-orientable compact surface of genus $n\geq 1$ has a two sheeted ...
3
votes
2answers
287 views

Non-orientable cover of a non-orientable surface

I was quite puzzled by the request of classifying all the $4$-covers of the connected sum of $5$ copies of $\Bbb R P^2$. For oriented covering space, the answer is well known: it's enough to consider ...