Talk:Foliation

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My comment on the introduction paragraph. Obviously I used 'stripes' because it is a very quick way to get a visual image of a foliation, locally, for anyone.

Charles Matthews 17:10, 8 Dec 2004 (UTC)

Right, but then you added a link to it, which I thought was very strange. I did entertain the notion it might be a technical term though and that's why I wrote my comment in my edit description. I removed the link to avoid possible future confusion, since I figured you were using the word informally.--C S 01:56, Dec 9, 2004 (UTC)

Well, WP can have an article on stripe, some day. There is no need to 'remove' red links, in fact. Charles Matthews 06:20, 9 Dec 2004 (UTC)

I wasn't removing it because it was a red link. Let me emphasize: I removed it to avoid future confusion. I shudder to think of somebody clicking on it and getting sent to a page about a candy store. For example, try Swirl. If you want to put it back, go ahead. I don't think there's a point to it though, since the second sentence pretty much gives a picture. --C S 06:38, Dec 9, 2004 (UTC)

Why? If anyone created a stripe page - which I have just done, by the way - it is their responsibility to make sure the backlinks from it are all useful. It is not your responsibility to stop them making some hypothetical mistake, which might distract some hypothetical reader some day. In fact that may remove some information they should have. The wiki isn't perfect; but the policy is that we assume editors are reasonable people first.

Charles Matthews 08:02, 9 Dec 2004 (UTC)

I see your point. --C S 08:45, Dec 9, 2004 (UTC)


Contents

[edit] foliation (geology)

I had a wild dream of having Foliation be a redirect page to foliation (disambiguation) and this page, which deals with mathematics, being called foliation (mathematical), and the gelogical us being foliation (geology). But with over 40 pages linking here on the math side and only 4 on the geology side, it seems silly. However, it is my request of fellow wikiers that the link to the diambiguation page be maintained at the top, as people interested in the geological usage can then go through to there and find foliation (geology. Its either that or someone will have to go the disambiguation route, which seems like a lot of work.
Cheers,
Rolinator 03:35, 30 December 2005 (UTC)

[edit] Hisotry of the subject

Does anyone about the history of foliation theory?

[edit] History of the subject

Does anyone know about the history of foliation theory? the book by Camacho and Neto says that it was invented as an attempt to solve Poincare's conjecture, but a theorem of Novikov shattered this hopes (every foliation of a closed 3-manifold with trivial, or finite?, fundamental group has a Reeb component). This book, or any other I know of, does not provide a reason why study/ do research on this subject. So, perhaps this entry would benefit if a reason to study foliations is provided.

I read somewhere that foliation theory was developed to understand the phase space structure of dynamical systems. Perhaps I can dig up some material on the subject. MathMartin 18:39, 26 September 2006 (UTC)

that would be great!

[edit] modification of the definition

I changed codimension by dimension, because I think that p is used in that sense in the definition.

It is confusing what p and n-p are for. From the definition, the dimension of leaves (or strips/plaques), where x=constant, should be p-dimensional, not n-p dimensional as stated. But this is inconsistent with what in Examples and Foliation... One has to either switch p and n-p in Definition, or those in later parts. I hope that I am not misunderstood...