Talk:Atlas (topology)

message: 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)

message: 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)
replies: text: 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)
replies: text: Thank you, Salix alba.  That was helpful. modify 06:19, 25 April 2006 (UTC)
thread_title:  Local patches 

message: 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)
thread_title:  Maximal atlas without Zorn's lemma 

message: Please see the page, User talk: Waltpohl, where I have made some comments regarding why this page should be rewritten.
Topology Expert (talk) 09:16, 12 August 2008 (UTC)
thread_title:  The article should be rewritten 

message: It seems Wikipedia does not have a topic on coordinate chart (which by the way redirects to atlas). However coordinate chart, by its own rights, is a quite vast subject. One should also talk about the flaws with charts (like singularities) which on the first place leads to the need of atlases.  —Preceding unsigned comment added by 158.130.104.26 (talk) 17:22, 3 February 2011 (UTC)
thread_title:  A separate topic on coordinate chart should be added 

message: … redirects to this article about atlases, but isn't mentioned anywhere in it.  — Preceding unsigned comment added by 93.231.173.68 (talk) 11:34, 9 August 2012 (UTC)
replies: text: Yep. We also have articles on smooth frames and on smooth structures, which do not define this either. The smooth frame article is about frames on the tangent bundle; it fails to generalize to general vector bundles. It also fails to mention atlases. This article defines the notion of "local" but never uses the word "local" in regards to that. It also never defines a frame' istead it hand-waves though the section "more structure". Sigh.  This article needs a major rewrite. 67.198.37.16 (talk) 04:51, 24 October 2016 (UTC)
thread_title:  Local Frame 

message: These days, its popular to define manifolds with sheaves and ringed spaces. At least some mention of this should be made here ... 67.198.37.16 (talk) 03:22, 2 October 2016 (UTC)
thread_title:  sheafs and ringed spaces 

message: An editor insists for inserting "The plural of atlas is atlantes" in the article. A scholar google search for "atlantes" manifold provides 138 hits, while "atlases" manifold provides 7410 hits. The page Manifold uses "atlases" including in section headers. Therefore, this edit is confusing, and breaks WP:NPOV, by pushing terminology that is rarely used. Therefore, I'll  replace this sentence by "the plural of atlas is atlases, although some authors use atlantes". This reflects the common usage. D.Lazard (talk) 10:07, 11 February 2018 (UTC)
thread_title:  Plural 

message: Our atlas should consist of charts that covers the manifold M, but in the article, we're covering some unspecified space X. The article even immediately states that the union of these charts covers the manifold after that.
Legatostaccato (talk) 05:51, 9 November 2019 (UTC)
thread_title:  Small correction to the formal definition?