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
Apple to unveil 'iWatch' on September 9
NASA deep-space rocket, SLS, to launch in 2018
Study examines 13,000-year-old nanodiamonds from multiple locations across three continents
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