Talk:Manifold

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Former featured article candidate Manifold is a former featured article candidate. Please view the links under Article milestones below to see why the nomination failed. For older candidates, please check the archive.
Article milestones
Date Process Result
November 18, 2005 Peer review Reviewed
January 31, 2006 Featured article candidate Not promoted
Current status: Former featured article candidate
WikiProject Mathematics (Rated B-class, Top-importance)
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Mathematics rating:
B Class
Top Importance
 Field: Geometry
One of the 500 most frequently viewed mathematics articles.
A selected article on the Mathematics Portal.
Version 0.5      (Rated b-Class)
Peer review This Math article has been selected for Version 0.5 and subsequent release versions of Wikipedia. It has been rated b-Class on the assessment scale.


Untitled[edit]

old: Talk:manifold/old, Talk:manifold/rewrite/freezer.


Impressed with this article[edit]

Since I usually nitpick on discussion pages, I just wanted to say that this article is very coherently constructed, provides good examples, and covers the topic well for a wide range of readers. Thank you to all who contributed to it. —The preceding unsigned comment was added by 24.205.231.209 (talkcontribs) 20:36, 2006 November 12.

Animated GIF[edit]

I've removed the animated GIF of "boy's surface" because of the distraction it causes. This action is consistent with MOS:ACCESS but counter to the wishes of User:Slawekb

https://en.wikipedia.org/w/index.php?title=Manifold&diff=581403804&oldid=581391247 : (The image and its caption accompany the text of the lead. If you don't like this particular image of Boy's surface, then find another one.)

Any opinions on this apart from the two of us?

-- Catskul (talk) 23:09, 14 November 2013 (UTC)

Presumably the onus is on you to make a more suitable image and convert the gif to video, per the guideline. The manual of style should not be used to dictate what kinds of informative content to have in articles. This image has informative value. Sławomir Biały (talk) 00:35, 15 November 2013 (UTC)
The real projective plane is a two-dimensional manifold that cannot be realized in three dimensions without self-intersection, shown here as Boy's surface.
As I understand it there is no onus on editors to replace offending content. If, for example, a statement is unsourced, an editor is not obligated to find a source which negates the content before removing. While the content I am attempting to remove has value, it is neither critical to the article nor mentioned anywhere in the text.
Despite my belief that replacement is not a requirement, consensus is needed. So in an attempt to achieve consensus, I suggest replacement of the original with the following:
-- Catskul (talk) 16:30, 15 November 2013 (UTC)
Aesthetically, that image is not really an improvement over what is there now. I will work on a better replacement when I get the time. Sławomir Biały (talk) 00:08, 16 November 2013 (UTC)
I'm going to add in an opinion here. The point that some 2d manifolds cannot be embedded in 3d space without self-intersection is not central to the concept of a manifold; it is an essentially topological result that applies only for an arbitrarily constrained choice of embedding space for a some manifolds. I'd say that a far more significant (or more generally applicable) points topologically are that manifolds can be closed or can be non-orientable, which are not even mentioned in the lead. I'd think that it would be sufficient to mention one or two illustrative cases such a the Klein bottle without mentioning properties of selected embeddings. —Quondum 13:01, 16 November 2013 (UTC)

I think the idea that there are 2-manifolds that are not realizable as surfaces in Euclidean space is actually quite important for understanding why there is a mathematical notion of "manifold" at all. Certainly, one can study manifolds without worrying about their embedding properties (although there are people who build their careers entirely on the latter), but to someone with no idea what a manifold even is, I think it is very important to realize that they do represent a significant generalization of the elementary notion of a surface. Sławomir Biały (talk) 13:31, 17 November 2013 (UTC)

The topological aspects of manifolds are important, I agree, but is only one of what they are useful for. The same point about embedding can be illustrated within a Klein bottle without challenging the reader nearly as much. Emphasizing the topological aspects at the expense of the geometric aspects is also not ideal. For example, the real projective plane also represents elliptic geometry, which does not come through at all. All these issues are complex enough that more than a mention in the lead can hint to the reader that this article is hard work to understand. —Quondum 21:32, 17 November 2013 (UTC)
Meanwhile I would second the removal of any animated gif until a suitable alternative can be found. These things do my head in really quite seriously, and I am sure I am not alone. Sometimes I can rely on my browser settings, but far from always. — Cheers, Steelpillow (Talk) 15:32, 12 January 2015 (UTC)

The surface of the Earth requires (at least) two charts to include every point[edit]

Not strictly true: the south pole (for example) can be depicted as a circle. — Preceding unsigned comment added by 92.2.211.93 (talkcontribs) 2014-10-16T17:39:48

Read the rest of the sentence. That circle is an example of "duplication of coverage". — Cheers, Steelpillow (Talk) 15:27, 12 January 2015 (UTC)

Realization?[edit]

The lead says that the Klein bottle and real projective plane cannot be realized in three dimensions. Where does this term "realized" come from? Sure they cannot be embedded/bijected, but they sure can be injected. In the theory of abstract polytopes the idea of "realization" describes all such injections into real space, however degenerate. Does topology differ, or should the lead be amended accordingly? — Cheers, Steelpillow (Talk) 15:23, 12 January 2015 (UTC)

Betti numbers and torsion coefficients[edit]

The topological characteristics of a manifold are captured in its Betti numbers and torsion coefficients. Only the first of these is mentioned in this article. I have started a discussion at Talk:Homology (mathematics)#Betti numbers and torsion coefficients and would be grateful for any contributions. — Cheers, Steelpillow (Talk) 15:37, 12 January 2015 (UTC)