Talk:Atlas (topology)
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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)
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, Ck, 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)