Talk:Topological manifold

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Contents 1 Attention needed 2 Separation from manifod entry 3 Merging to manifold 4 composition link 5 5-manifold?

[edit] Attention needed

MarSch created this as a cut&paste from manifold, and that's still where we are, an incoherent mess. Any work on this article is much appreciated. Oleg Alexandrov (talk) 16:59, 22 December 2005 (UTC)

"A topological manifold is a manifold that is glued together from Euclidean spaces"? A piece of paper is a Euclidian space, therefore if I glue a bunch of papers together I get a topological manifold? Serious need of attention, yes, granted. FelisSchrödingeris 14:45, 7 April 2006 (UTC)

I'm wondering where you get that quote from. It certainly isn't in the article of the date of your comment and I can't find it in the early versions. I do kind of recall saying something like that somewhere though. --MarSch 17:56, 15 April 2006 (UTC)

As a matter of fact, it's the first line of the article in it's present form. The analogy used in my comment perhaps wasn't quite relevant (although it was the first thing that popped into my head while reading it), but the idea behind it still holds...

The concept, I gather, is a basic one in the field of topology. But that sentence alone pre-supposes that the reader knows what a "manifold" is. It also uses the concept of "gluing of Euclidian spaces", which, for a non-topologist like me, doesn't make much sense. A good introduction - a gentle slope into the concepts - is mainly what's missing, I guess. FelisSchrödingeris 14:36, 18 April 2006 (UTC)

Manifold is supposed to explain the gluing. Then this article only needs to specify that the what which is being glued are the topologies of Euclidean spaces. That's why things are as they are. There are so many different kinds of manifold that it is a huge duplication of effort to explain the gluing in each one separately.--MarSch 08:59, 19 April 2006 (UTC)

How about creating glueing, which is in Wikipedia:Missing science topics/Maths4. Oleg Alexandrov (talk) 17:04, 19 April 2006 (UTC)

Interesting suggestion. What would manifold be for if we create glueing? --MarSch 11:43, 20 April 2006 (UTC)

This is now a stale thread, but topology does a great deal of gluing (correct spelling) that is not suitable for manifolds. For a manifold we must have overlapping open sets, but in the more general concept we can glue two circles together at a single point, creating a "figure-8", or glue edges of a polygon together to create an orbifold. Other fun (and useful) objects we can create in this way include a bouquet of spheres and a CW complex. --KSmrq^T 07:50, 21 November 2006 (UTC)

[edit] Separation from manifod entry

Can anybody explain to me briefly what should be in this entry in distinction to the manifold entry. Then I may be able to clean up a little bit. Hottiger 11:03, 14 April 2006 (UTC)

Besides: The example fo the hausdorff condition should clarify the topology imho. Hottiger 11:03, 14 April 2006 (UTC)

Gladly. Long ago some mathematician editors decided that manifold was supposed to be about the general concept of manifold exemplified by such concrete entities as topological manifolds, differentiable manifolds, complex manifolds and arguably algebraic varieties and schemes. The common thing being that you go from something well understood to something new by gluing well understood objects together. Because these editors thought that this was actually explainable to non-mathematicians it was decided to designate manifold as the article in which to do this and not focus on exact definitions (which don't exist for this concept) or technicalities or whatever else might stand in the way of comprehension. So manifold is supposed to explain only this process (of gluing). Of course the gory details need to be discussed somewhere too, and this article is supposed to contain them. I hope this clarifies. --MarSch 18:07, 15 April 2006 (UTC)

That is, what seemed to be the initil intention. The result is that the initial explaining image in the manifold entry explains what is a 2-dimensional Reimannian manifold (there are ankles shown). In my opinion, the entry isn't good neither for non-mathematicians nor for mathematicians. By the way, one should not even try to explain what a scheme is in a manifold entry. Hottiger 17:43, 4 October 2006 (UTC)

[edit] Merging to manifold

See Talk:Manifold#Merging from topological manifold Oleg Alexandrov (talk) 15:26, 2 May 2006 (UTC)

[edit] composition link

Can someone clarify what exactly is meant by the composition link? There are three separate definitions for mathematics-related composition on the disambig page, and so the link as it is not very helpful. All we need to know is what definition the author was using for the word. SingCal 06:58, 27 July 2006 (UTC)

Function composition. I disamb'ed the link; thanks for your note. -- Jitse Niesen (talk) 09:34, 27 July 2006 (UTC)

Thanks!! SingCal 21:42, 27 July 2006 (UTC)

[edit] 5-manifold?

I had just seen an article: 5-manifold. I wondered if it should be listed under, "See Also" If so, it looks like it needs a bit of work.Brian Pearson 07:15, 21 November 2006 (UTC)