Foliation, fibration, fiber bundle?

  • Thread starter jojoo
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Main Question or Discussion Point

what's the difference among those three objects?
Any body can give me some examples?

Thanks
 

Answers and Replies

Both a foliation and a fibration of a manifold are a division of the manifold into sets of equivalence classes. For a foliation the equivalence classes can be topological different but for fibration they must be the same. A fibration gives the original manifold the structure of a fiber bundle, with each equivalence class being a fiber. The equivalence classes of a foliation are called leaves.

For a simple example, let [itex]r[/itex] be the distance to some point in the plane. Then the sets [itex]\{r=\text{const}\}[/itex] are a foliation, with leaves being circles and a point. If the point is excluded from the plane - turning it into a punctered plane - this will be a fibration.
 

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