Talk:Atlas (topology)

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Mathematics rating:	Stub Class	Mid Priority	Field: Topology
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. needs expansion, wikification, refs, and organisation--Cronholm144 09:18, 23 May 2007 (UTC)

The definition of a differential structure by means of a maximal atlas is the one I learned first. I recall some other definition, as a sheaf cohomology H¹ class; with respect to some sheaf built from diffeomorphisms. This does seem to have advantages - perhaps I'm wrong. Anyway, I'd quite like to see this idea in Wikipedia.

Charles Matthews 15:42, 14 Jun 2004 (UTC)

Contents 1 manifold atlas? 2 Can anybody fix this sentence? 3 Local patches 4 Maximal atlas without Zorn's lemma

[edit] manifold atlas?

Does atlas have any meaning besides the one in the definition of a manifold? If not perhaps we should integrate it into manifold. Both articles would benefit from some more context. --MarSch 14:30, 2 Jun 2005 (UTC)

One can talk about G-atlases on fiber bundles. Anyway, I think it's probably better to keep this page separate. Even for manifolds, we can have different kinds of atlases depending on what kind of manifold we have (topological, C^k, smooth, real-analytic, complex-analytic, etc.) -- Fropuff 14:57, 2005 Jun 2 (UTC)

The technical details about atlases are I think better discussed in a stand-alone article, as this one. The manifold article is already long and in some places quite complicated, no need to make it even more so. Oleg Alexandrov 22:27, 2 Jun 2005 (UTC)

perhaps manifold and fiber bundle both need a section on atlases? There is currently one article for topological manifolds and differentiable manifolds. Maybe we should split that up. --MarSch 10:57, 3 Jun 2005 (UTC)

It is good that manifold starts with a discussion of topological manifolds before going to differential manifolds. Being a topological manifold is a big part of what a differential manifold is about, so you can't really avoid it. Splitting things up will make the concept of differential manifold harder to understtand. That's my take. Oleg Alexandrov 15:49, 3 Jun 2005 (UTC)

Yeah, well I don't really want to split them up, since I like to merge articles. I am a bit surprised that you don't want to split. Just defaulting to disagreeing with me ;) ? --MarSch 16:23, 3 Jun 2005 (UTC)

If you mean that've been bugging you too much lately, then you are right. I will try to take it in a more relaxed way. Oleg Alexandrov 04:34, 4 Jun 2005 (UTC)

PS But I still stand by my opinon above. Oleg Alexandrov 04:34, 4 Jun 2005 (UTC)

[edit] Can anybody fix this sentence?

"For each point in the complicated space, a neighborhood of that point that is homeomorphic to a simple space. The homeomorphism is called a chart."

[edit] Local patches

The term local patch in Metric tensor (general relativity) redirected to Chart (topology) which redirected to here. Is the term a synonym for something in the article? modify 19:28, 24 April 2006 (UTC)

Yep. Basically the coordinate system for a local patch is defined by a chart (a map from part of Rⁿ to the local patch), the coordinate system for Rⁿ is mapped to give coordinates for the local patch. An atlas is the set of all the charts. See Manifold for a more extensive discussion aimed at a general audience. --Salix alba (talk) 23:31, 24 April 2006 (UTC)

Thank you, Salix alba. That was helpful. modify 06:19, 25 April 2006 (UTC)

[edit] Maximal atlas without Zorn's lemma

The article claims the existence of a maximal atlas without using Zorn's lemma. But the only given reference uses it and I only know proofs of it's existence making use of Zorn's lemma. Could somebody give a reference to a source, that shows existence without it? 129.241.128.205 (talk) 22:17, 7 May 2008 (UTC)