Talk:Orientability

message: Don't you miss (the capacity of) orientation - a basic condition of a sane person?
Apogr 10:53, 2 Sep 2004 (UTC)
replies: text: No. Elroch 18:12, 15 February 2006 (UTC)
thread_title: 2004

message: The previous version of this page stated that, to orient a triangulated surface, it is equivalent to orient each triangle so that identified edges point in the same direction. In fact, they should point in the opposite direction. The picture to have in your head is that all the triangles are oriented clockwise (for example). If you have two clockwise oriented triangles in the plane, and you glue them along an edge, the edge will be oriented in opposite directions in first triangle and the second.
18.87.1.112 (talk) 16:04, 6 May 2010 (UTC)
thread_title:  Explanation of correction in triangulation section 

message: There has been a merge tag on Orientable manifold for a long time.  I don't know the subject well enough to comment, but could someone who does start a discussion to resolve the proposition? Kcordina 12:29, 17 March 2006 (UTC)
replies: text: Comment for readers: This has already been done; orientable manifold redirects here.  --C S (Talk) 04:25, 12 April 2006 (UTC)
thread_title: Merge?

message: As far as I know, the difference from the critical density of the universe has not yet been measured, thus whether the universe is closed or not is completely up in the air.  Anyway, it's not really relevant, so I'm removing it. -lethe talk [ +] 06:03, 13 April 2006 (UTC)
replies: text: It appears to me also that this is a controversial claim to make, so it's good to remove it.  --C S (Talk) 13:09, 13 April 2006 (UTC)
thread_title:  universe is closed 

message: I was also looking suspiciously at the recent anonymous edit that Oleg reverted, which changed "manifold orientable iff its tangent bundle is" to "tangent bundle always orientable".  Oleg says that Mathworld's article agrees with the original.  I myself am a little bit confused.  I know for sure that the cotangent bundle of any manifold is always orientable, indeed even carries a choice of orientation.  I think it's believable that the tangent bundle could also be orientable, Does not the orientation on the cotangent bundle also induce an orientation on the tangent bundle?  I'm gonna poke in some books (mathworld isn't definitive). -lethe talk [ +] 04:17, 22 May 2006 (UTC)
replies: text:  Yes, the cotangent bundle is always orientable, per planetmath, see at the bottom. I don't know details though. :) Oleg Alexandrov (talk) 04:22, 22 May 2006 (UTC)
replies: text: The proof that the cotangent bundle is easy: there exists a canonical symplectic form on any cotangent bundle.  Any symplectic manifold is oriented.  How's this for a proof for tangent bundles: every second-countable Hausdorff manifold admits a Riemannian metric.  Every Riemannian metric induces an isomorphism between the cotangent bundle and the tangent bundle.  The cotangent bundle is always oriented, so the tangent bundle is too.  Mathworld is wrong (haven't found it in my books yet though). -lethe talk [ +] 04:26, 22 May 2006 (UTC)
replies: text:  My theory is that since the orientation of a manifold is defined as an orientation of tangent vector spaces, someone over at mathworld got confused and thought that the orientation of a manifold and its tangent bundle (which is after all a disjoint union of tangent vector spaces) were the same thing.  This isn't right: the orientation of a manifold is defined in terms of its tangent bundle.  The orientation of the tangent bundle is defined in terms of the tangent bundle of the tangent bundle, which is a different object.  Someone at mathworld made that mistake and it propagated to us, that's my theory.  Anyway, I like my easy proof above well enough to be convinced of its rightness.  Comments welcome. -lethe talk [ +] 04:35, 22 May 2006 (UTC)

text: Ah yes.  That makes perfect sense, I probably should have known that right away.  OK, yes, that needs to be made clear in the article.  So anyway, the statement "a manifold is true iff its tangent bundle is orientable" is trivially true because it's the definition of orientability for manifolds. -lethe talk [ +] 00:11, 24 May 2006 (UTC)
replies: text: I've reworked that short section.  Comments welcome. -lethe talk [ +] 00:28, 24 May 2006 (UTC)
thread_title:  tangent bundle always oriented? 

message: I don't understand the difference : "An orientable surface is an abstract surface that admits an orientation, while an oriented surface is a surface that is abstractly orientable, and has the additional datum of a choice of one of the 2 possible orientations."  —Preceding unsigned comment added by 82.252.12.212 (talk) 11:42, 11 July 2008 (UTC)
replies: text: Consider a sphere in R3.  An orientation on the sphere is given by a unit vector normal to the surface.  The sphere is orientable since it is possible to do this.  However, it is not oriented until you say which unit vector you are going to use: the outward normal or the inward normal.  siℓℓy rabbit (talk) 13:09, 11 July 2008 (UTC)
thread_title:  oriented vs orientable 

message: We can use normal vectors to define orientablity in an intuitive way. It's better to  mention at this article.--刻意 09:57, 25 December 2008 (UTC)
thread_title: Another approach for co-dimension 1 surfaces

message: I found this article's beginning to be quite confusing. It does not make sense to those not experienced in the field of mathematics. Would it be possible to create a "common language" explanation as well?
What do I mean by that? I am referring to some of the sections in other mathematical articles, such as the division by zero article. They have a complex explanation of the problem as well as a basic one comprehendable to those who have at least some basic understanding of math. Could this article have a similar section too? Fusion7 (talk) 19:20, 23 August 2009 (UTC)
thread_title:  very confusing. 

message: In the paragraph "topological definitions" it is stated: an orientable manifold is one whose structure group [...] can be reduced to the subgroup GL+(n) [...]. The only way I can understand this is by thinking of the tangent bundle, but in a paragraph about topological, not differentiable, manifolds, this would not make sense. Should the sentence be removed, perhaps? --83.228.202.2 (talk) 13:13, 11 March 2012 (UTC)
thread_title:  Unclear statement 

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thread_title:  External links modified 

message: Why are smooth surfaces which contain an open set diffeomorphic to mobius band , non-orientable ? Abhinna Sundar (talk) 14:33, 10 November 2018 (UTC)
thread_title:  Non orientablitlity