Talk:Manifold/old

message: Lost in the debate was my primary objections to MarSch's edits. First was cutting the "intrinsic vs extrinsic part"; that still to be discussed. The second was the "cleanup" taken by MarSch as result of which charts were defined first and the treatment of topological manifolds and differential manifolds were rather combined. Now I reverted that to the way it was before. More work is needed, but this is a better starting point. Oleg Alexandrov 21:27, 26 May 2005 (UTC)
replies: text: I stared at the article a bit more and I do like the old version better. It flows. Whereas, in MarSch's edits the stuff about charts seemd suoperfluous (its already wikilinked to the right article), and the topology discussion got interrupted by statements about differentiability before moving back to topology.  However, the article does have problems, I'll list below.   (Sorry to take so long to respond. I've gotten hopelessly tangled in stupid VfD issues, see Harmonics theory. I normally run away from controversy. Sigh.) linas 05:10, 2 Jun 2005 (UTC)
thread_title:  Recent changes 

message: I would like to see Atlas (topology) expanded; the layman's intro is good, but a good mathematical definition would be a lot better.  e.g. a discussion of the transition functions, and a discussion of the Jacobi identity-like thing  (the Bianchi identity-like thing?) or whatever its called where you have three open sets intersecting, and the charts have to be three-way consistent.  Maybe MarSch could apply himself there?  linas 05:35, 2 Jun 2005 (UTC)
replies: text: I concur.  The detailed material on atlases is better placed in the separate atlas article where they can be given a thorough treatment without interrupting the flow of this article.  I suggest perhaps using the section called "Additional structures and generalizations" to (briefly!) give a description of differentiable manifolds, and then a link to a separate article: differentiable manifolds.  My view is that we should relegate all additional structures not present in the basic definition of topological manifolds to separate articles. - Gauge 04:11, 5 Jun 2005 (UTC)
replies: text:  I propose to wait moving everything to a separate article until the sections here get "too big", and not because of lack of headings. Since we need to summarize these articles here anyway I see little point in splitting of things which are too small to summarize. --MarSch 11:49, 5 Jun 2005 (UTC)
thread_title: Charts

message: Article states: (Readers should see the topology glossary for definitions of topological terms used in this article.)  Can we cut this sentence out? linas 05:23, 2 Jun 2005 (UTC)
replies: text: This was added before we had articles on the individual terms. It's no longer needed, so I've removed it. --Zundark 09:39, 2 Jun 2005 (UTC)
thread_title: Misc article problems

message: Article states: ...it is tempting to think that being locally homeomorphic to a Euclidean space implies being a Hausdorff space. A counterexample is created by deleting zero from the real line and replacing it with two points, an open neighborhood of either of which includes all nonzero numbers in some open interval centered at zero. This construction, called the real line with two origins is not Hausdorff, because the two origins cannot be separated.
These sentences seem to imply that the "real line with two origins" is homeomorphic to the real line.  It is not clear that it is, or that it isn't. Wording should be fixed. linas 05:23, 2 Jun 2005 (UTC)
thread_title: Hausdorff

message: Just an idea, but maybe the article should provide a few sentances on differential geometry and calculus on manifolds, maybe mentioning that a manifold has concepts of area and volume? linas 06:06, 2 Jun 2005 (UTC)
replies: text: Well, it doesn't really. Charles Matthews 10:07, 2 Jun 2005 (UTC)

text: To be pedantic, what a smooth manifold has is a class of Lebesgue measures, such that every diffeomorphism leaves the class invariant. So volume forms are defined up to smooth invertible functions. But that's not the same as having a preferred volume form. Charles Matthews 12:49, 2 Jun 2005 (UTC)
replies: text: Didn't mean to suggest there is a natural volume form; what I'm trying to suggest is that half the stuff in the section on differentiable manifolds should be moved to the article on charts, and that instead a paragraph or two should be added on calculus on manifolds.  Surely a mention of calculus on manifolds is more important and interesting that algebra of scalars which is neat and all that but of somewhat lower priority.  Since we appear not have a calculus on manifolds article, I figured that at a bare minimum, the article on volume form is at least not embarassingly thin and thus linkable. Also, adding your pedantic defn. above to the article seems maybe worthwhile. I dunno. linas 06:25, 4 Jun 2005 (UTC)

text: I think you mean to mention things like Differential forms and tensor fields and I agree. --MarSch 12:01, 5 Jun 2005 (UTC)
thread_title: [[Volume form]]

message: Wording needs to be fixed and clarified. For a Ck manifold M, you can form the Ck functions to the real or complex numbers. What does "..to the.." mean?  Which Ck functions are these? Are these the charts? Are these some other functions defned on the manifold? Its known that the set of scalar-valued functions on a manifold form an algebra, is that what this paragraph is talking about? linas 06:06, 2 Jun 2005 (UTC)
replies: text: The functions with k derivatives, basically: see smooth function. The kth derivative is assumed continuous. Charles Matthews 10:06, 2 Jun 2005 (UTC)
replies: text:  The sentence above is indeed mathematically correct, but I would say not well worded. It is not whether "you can form" the functions; they exist whether you want it or not. And indeed, saying "to the reals" sounds clumsy, better say "real-valued". I modified this in the article, wonder how it looks now. Oleg Alexandrov 14:55, 2 Jun 2005 (UTC)
replies: text:  Thanks Oleg. Charles, due to the recent edit controversy, I just thought I'd jot down a list of to-do cleanup items for this article; the questions were rhetorical. linas 06:17, 4 Jun 2005 (UTC)
thread_title: Algebra of scalars

message: Should this article mention (probably in the "see also" section) algebraic variety ?  Or at least algebraic geometry? linas 06:06, 2 Jun 2005 (UTC)
replies: text: At least in the see also section algebraic variety. Don't know about alg. geom. --MarSch 11:51, 4 Jun 2005 (UTC)
thread_title: [[Algebraic variety]]

message: I find this section in the article not very helpful. I mean, all the other sections talk about really important concepts about manifolds (tangent space, classification); this one I think is a minor thing, and I belive we could be better off without it. Comments? Oleg Alexandrov 16:52, 4 Jun 2005 (UTC)
replies: text: Agreed.  It seems out of place here as a separate section. - Gauge 04:16, 5 Jun 2005 (UTC)

text: You can preserve that information, but in a different place. As you said, you don't know how to expand that section, or how to explain its significance. So for now, we are better off without it. Oleg Alexandrov 15:17, 5 Jun 2005 (UTC)
replies: text: I _have_ just explained its significance. You can stick a sect-stub on it if you want. --MarSch 16:47, 9 Jun 2005 (UTC)

text: Actually this section is also a prerequisite for the exterior calculus that linas wants to add, since these are the 0-forms. --MarSch 16:54, 9 Jun 2005 (UTC)
thread_title: Algebra of scalars

message: *I think that a good article on manifolds should not ignore charts.MarSch
: I thought the section ==Differentiable manifolds== mentions charts in the right place. Where else would you want them? Oleg Alexandrov 16:47, 4 Jun 2005 (UTC)
replies: text: topological manifolds also have charts. Transition maps are automatically homeomorphism. There is stuff we can say about charts and we should make a section for that. When it grows too large we can split off some to the article about charts, but we are not there yet. Charts are also "really important". --MarSch 11:40, 5 Jun 2005 (UTC)
thread_title: Charts

message: Any of you maths genii feel like writing some kind of article on Frölicher spaces?  I would, but as soon as I see math where numbers start getting replaced by letters, I break out in cold sweat.  I only ask cause it's on the list of Articles requested for more than two years.  Ta.  Proto t c 4 July 2005 12:44 (UTC)
:I would if I knew what it is. Googling didn't really help. Anyone else? --MarSch 7 July 2005 11:23 (UTC)
This link is a start.  Check the bottom of page 16 for the definition.  It seems to be a part of synthetic differential geometry.  See  this for the associated philosophy.  - Gauge 21:05, 10 July 2005 (UTC)
thread_title:  Frölicher space 

message: Please insert a layperson definition of a manifold. if you can understand the technical description below, you probably already know what one is... --anon user (moved here by Oleg Alexandrov 23:05, 28 July 2005 (UTC)
replies: text: See manifold/rewrite. You can address your questions at Talk:Manifold/rewrite. Oleg Alexandrov 23:05, 28 July 2005 (UTC)
thread_title:  Simple description 

message: It looks to me that Deryck Chan copied over manifold/rewrite to manifold, and without any discussion or edit summary. Is that the right thing to do? Oleg Alexandrov 00:24, 4 August 2005 (UTC)
replies: text: The collaboration period finished, therefore we've to move the collaborated results from the rewrite page back to the article page. However, of course, due to differences betwen the 2 versions, more sum-up edits are required to furnish up the article. Deryck C. 05:31, 4 August 2005 (UTC)
replies: text: I beg your pardon? The rewrite is largely independent of the maths COTW (which is what I suppose you mean with "collaboration"); it was started before manifold was selected as the collaboration. I think you should at least have discussed it. -- Jitse Niesen (talk) 10:31, 4 August 2005 (UTC)
replies: text:  Agree with Jitse. Please understand that the rewrite has been going for much longer than the current collaboration of the week, you have no knowledge of how this started or what its purpose is, as such, I think you should have looked more closely into the matter before doing the merge, or otherwise left it alone. Oleg Alexandrov 15:32, 4 August 2005 (UTC)
replies: text: So leave it alone, however after all I disagree with the idea of a separate rewrite page. Deryck C. 06:19, 6 August 2005 (UTC)
thread_title:  No rewrite anymore 

message: Despite the fact that the talk page prominently says a rewrite is in progress, some folks have continued to edit this page. Either they are wasting their time, or someone is going to have to try to integrate their edits into the rewrite — and it ain't gonna be me! Thus the warning language spells it out unambiguously, so no one can complain when the edits are lost. Parallel efforts make no sense. KSmrq 22:05, 2005 August 6 (UTC)
Therefore, as I say, we should NOT have a separate rewrite page. Deryck C. 09:34, 7 August 2005 (UTC)
replies: text: Deryck, you have a point. I usually don't agree with rewrites on separates pages either. However, this was special. If you take the time to read this talk page from the very top, you will understand why (and don't forget, an edit summary and discussion matter :) Oleg Alexandrov 23:40, 7 August 2005 (UTC)
replies: text: Well, it seems that you misspell my name on alternate times... =_= Deryck C. 08:51, 8 August 2005 (UTC)

text: Never mind, I never meant to blame you. It's just a bit funny to get it correct on the first time but misspell it on the second time. Deryck C. 03:27, 9 August 2005 (UTC)
thread_title:  Wording of warning 

message: I applaude the effort, but if you don't want the page edited, why not request to have it locked? And why not just do a straight merge? I can do this at any point if so requested. - Ta bu shi da yu 04:18, 9 August 2005 (UTC)
replies: text: I've done this before and got reverted. Deryck C. 04:39, 9 August 2005 (UTC)
replies: text:  I thought that the moral of the story was that one should ask first. Ta bu shi da yu has a point. Let us see what others say. Oleg Alexandrov 04:53, 9 August 2005 (UTC)
replies: text:  Is there a way to merge the histories? Just wondering. Oleg Alexandrov 04:54, 9 August 2005 (UTC)
replies: text: Merge histories? No. Deryck C. 05:35, 9 August 2005 (UTC)

text: I do think the rewrite is ready to replace the old version and have said so at the rewrite --MarSch 16:26, 14 August 2005 (UTC)
replies: text: Depends on the person who advocated this rewrite. Deryck C. 00:50, 18 August 2005 (UTC)
thread_title:  How far till this is done? 

message: I have marked this page for deletion - subpages do not belong, and are in fact disabled, in the main article space.  I landed here by clicking random article, yet this is not an article, but an archived version of one.  If it is meant to be a freestanding article, that represents a content fork from Manifold, which should not exist.  If it is here merely as a resource for people working on Manifold, it should exist only in user or talk namespace, not in the main article namespace.  I am posting here to alert anyone who may care about this content to move it to a different namespace before it is deleted. — Swpb talk contribs 06:42, 17 January 2007 (UTC)
thread_title: This doesn't belong here