# Foliation, fibration, fiber bundle?

by jojoo
Tags: bundle, fiber, fibration, foliation
 P: 4 what's the difference among those three objects? Any body can give me some examples? Thanks
 P: 52 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 $r$ be the distance to some point in the plane. Then the sets $\{r=\text{const}\}$ 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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