Timeline for Foliated bundles and suspensions
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 24, 2010 at 1:46 | comment | added | Indrava Roy | Hi! Thanks a lot for your replies! @Dmitri: I'm sorry I didn't know that these terms are not widely used, the definition of a foliated bundle can be found in the link given by jvp or at foliations.org/surveys/FoliationLectNotes_Milnor.pdf. The term "foliated flat bundle" is mentioned in the Survey article by Kordyukov here: arxiv.org/PS_cache/math/pdf/0504/0504095v2.pdf @Tom: Sorry for the confusion. | |
| Jan 24, 2010 at 1:14 | comment | added | Tom Church | Thanks for catching that! Actually for F noncompact the definition of "foliation transverse to the fibers" is often taken to require that each leaf cover the base (e.g. "Geometric Theory of Foliations", p.91), but that's not at all obvious from the terminology, so it's a good point to emphasize. | |
| Jan 24, 2010 at 1:02 | history | edited | Jorge Vitório Pereira |
edited tags
|
|
| Jan 24, 2010 at 1:01 | history | edited | Jorge Vitório Pereira |
edited tags
|
|
| Jan 24, 2010 at 0:56 | comment | added | Jorge Vitório Pereira | Tom, your iff is not exactly right. If F is not compact then leaves can scape to infinity preventing the lift of paths from the base to them. | |
| Jan 24, 2010 at 0:47 | answer | added | Jorge Vitório Pereira | timeline score: 3 | |
| Jan 24, 2010 at 0:43 | comment | added | Tom Church | I'm confused by your terminology. If F -> E -> B is a bundle of manifolds with dim F = n, then the bundle is flat (i.e. arises from a map pi_1(B) -> Diff(F) by your construction) iff E admits a codimension n foliation transverse to the fibers. Proof: monodromy. Can you give an example of a "foliated bundle" (in your terminology) which is not a "foliated flat bundle"? | |
| Jan 24, 2010 at 0:36 | comment | added | Dmitri Panov | Indrava, could you please explain what is a foliated bundle, or foliated flat bundle? I don't think these are completely standard math expression (at least I don't know what they mean). | |
| Jan 23, 2010 at 23:47 | history | asked | Indrava Roy | CC BY-SA 2.5 |