1. Do I understand correctly that closed curves on a 3-dimensional torus are represented as closed ribbons lying freely (with the possibility of inverting) on a classical torus?
2. Do I understand correctly that if all the isotropic straight lines of a Minkowski space are mapped on the corresponding circles, then the isotropic cone is mapped on the product S2 x S1, and if all the isotropic straight lines of a 4-dimensional space with a neutral metric are mapped on the corresponding circles, then the isotropic cone turns into a 3-dimensional torus? Finally, is it true that with this compactification of an 8-dimensional space with a neutral metric, we get a product S3 x S3 x S1 instead of a cone?
A small correction: in all these cases, the cone turns into a bouquet of two products of spheres, for example, when compactifying the pseudo-Euclidean plane, we get a bouquet of two circles.
The questions asked are closely related to the previous one:
Tpological foundation of the standard model
https://www.researchgate.net/post/Tpological_foundation_of_the_standard_model
- Badges
- Science topic
- Similar topics
- Geoscience
- Cartography
- Mapping