Register to reply

Foliation, fibration, fiber bundle?

by jojoo
Tags: bundle, fiber, fibration, foliation
Share this thread:
jojoo
#1
Apr12-08, 08:24 PM
P: 4
what's the difference among those three objects?
Any body can give me some examples?

Thanks
Phys.Org News Partner Science news on Phys.org
Security CTO to detail Android Fake ID flaw at Black Hat
Huge waves measured for first time in Arctic Ocean
Mysterious molecules in space
OrderOfThings
#2
Apr28-08, 01:33 PM
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 [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.


Register to reply

Related Discussions
A bit introduction to foliation in GR and some question. Special & General Relativity 1
What is a Vector Bundle? Differential Geometry 3
Glass fiber v's carbon fiber Materials & Chemical Engineering 0
A Toy Principle Bundle Differential Geometry 2
Principal G-bundle and bundle of bases (footnote) General Math 2