# Foliation, fibration, fiber bundle?

1. Apr 12, 2008

### jojoo

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

Thanks

2. Apr 28, 2008

### OrderOfThings

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.