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Probably not. I just took the first word that came to mind. I would likely use path so that I directly have a parameterization to work with - just in case. It avoids reediting.martinbn said:
What is the 4D Equivalent of a Möbius Strip or Klein Bottle?
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SUMMARY
The discussion centers on the exploration of higher-dimensional analogs of the Möbius strip and Klein bottle, specifically questioning what a 4D equivalent might be. Participants agree that while the Möbius strip is a 2D non-orientable surface and the Klein bottle is a 3D non-orientable manifold, the 4D equivalent could be represented by real projective space or a generalized Klein bottle. The conversation highlights the complexities of embedding these manifolds in various dimensions, with references to the Whitney Theorem and the concept of quotient spaces.
PREREQUISITES- Understanding of non-orientable surfaces, specifically the Möbius strip and Klein bottle.
- Familiarity with manifold theory and dimensions in topology.
- Knowledge of quotient spaces and their construction in topology.
- Basic understanding of the Whitney Theorem regarding manifold embeddings.
- Research the properties of real projective space as a 4D manifold.
- Study the implications of the Whitney Theorem on manifold embeddings in higher dimensions.
- Explore the concept of generalized Klein bottles and their construction from cubes.
- Investigate the characteristics of non-orientable flat three-manifolds and their embeddings.
Mathematicians, topologists, and students interested in advanced geometry, particularly those exploring the properties and applications of non-orientable surfaces and higher-dimensional manifolds.
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