Talk:Spin structure

message: I removed the following paragraph, since it certainly didn't belong in the intro, and it may not even belong in the article at all:
:In particle physics the spin statistics theorem implies that the wavefunction of an uncharged fermion is a section an associated vector bundle to a the spin lift of an SO(N) bundle E.  Therefore the choice of spin structure is part of the data needed to define the wavefunction, and often needs to be summed over in the partition function.  In many physical theories E is the tangent bundle, but for the fermions on the worldvolumes of D-branes in string theory it is the normal bundle. 
Silly rabbit 19:55, 21 June 2006 (UTC)
replies: text: Spin structures are important in particle physics.  Particle physics in turn was crucial to the history of spin structures, the name term "spin structure"  itself I think owes its origins to particle physics.   So the connection between the two I think needs to appear in the article, if not in the introduction, although I agree that the above paragraph is too technical for an introduction.  Perhaps a compromise would be a nontechnical sentence in the introduction and then the above paragraph can be put in a particle physics subsection analogous to that in the spin^c section. --JarahE 07:35, 2 July 2006 (UTC)
replies: text: Fair enough.  Shall we create a Spin structures in particle physics section (or such-like), and point it out in the intro? Silly rabbit 19:12, 2 July 2006 (UTC)
replies: text: I vote to keep Spin-c here.  Morally, these are just another "kind" of "spin" structures (a propos of spinors). Silly rabbit 21:36, 2 July 2006 (UTC)

text: Ok, so then maybe we should put in a redirect so that people searching for spin^c structures get here?  I'm not sure how to do this with the superscript, maybe redirect all of the various ways that people could try to type it? JarahE 12:02, 3 July 2006 (UTC)
thread_title:  This seemed out of place 

message: We have some problems developing in the spin^c part of this article. I think the problem is Sławomir Biały is editing an article that has a less general definition of spin^c structure than he would like.  Currently the definition is only for orientable bundles but he seems to be editing for a more general notion of spin^c structure.   IMO there's no point in putting in results about a notion of spin^c structure that hasn't been defined in the article.  Rybu (talk) 17:51, 20 May 2009 (UTC)
replies: text: Yes, you're right.  I was confused.  The Gompf article doesn't appear to give details on the correspondence.  The Lawson and Michelsohn text gives a construction in which spinc structures naturally correspond to elements of 2H^2(M,\mathbb{Z})\oplus H^1(M,\mathbb{Z}_2).  It could be that when the obstruction vanishes, this can be put into correspondence with H^2(M,\mathbb{Z}); however, I believe it has been said somewhere that the correspondence of spinc structures with H^2(M,\mathbb{Z}) is not natural.  Sławomir Biały (talk) 21:46, 20 May 2009 (UTC)
thread_title:  spin^c nonsense 

message: You are starting the article Spin structure considering spin structures on vector bundles, but a (classical) spin structure on an oriented Riemannian manifold M is a spin structure on its tangent bundle TM (this is also the definition of spin manifold, see Lawson and Michelson (1989) "Spin Geometry" [page 78 (Spin Structures on Vector Bundles) and page 85 (Spin Manifolds and Spin Cobordism)]. I think is much better to start with a "classical definition" of spin structure, using principal fibre bundle, cf. Thomas Friedrich in "Dirac Operators in Riemannian Geometry" (2000), page 35. This is also the original definition given by A. Haefliger, Sur l’extension du groupe structural d’un espace fibré, C. R. Acad. Sci. Paris 243 (1956)
558–560. For spin^c structure cf. (again!) Thomas Friedrich page 47.
Mgvongoeden 16:52, 8 June 2011 (UTC)
thread_title:  Spin structures (starting with principal bundles) 

message: Substituted at 21:59, 26 June 2016 (UTC)
thread_title: Assessment comment

message: The section on Vector structures is very confusing and not clearly written. It should be either written in more rigorous and precise terms or erased. SupergravityGuy (talk) 00:29, 14 July 2016 (UTC)
thread_title:  Vector structures 

message: This article doesn't clearly answer the question what is a spin structure, and it relies/references heavily the article on spinor bundles, which in turn relies heavily on this article. For example, the first paragraph describes what you can do with spin structures, the second paragraph describes why they are useful in particle physics and mathematics generally.  The overview then starts with a requirement for their existence, then a paragraph about spinor bundles (again circular reference), then some history that fiber bundles needed to be defined first.
Finally there is a partial definition in the section "Spin structures on Riemannian manifolds". Of course this is a qualified definition, but it is the first non-circular one.
Yes, I also came here wondering what a spin structure is, and the circular nature of the article was no help at all. Kbk (talk) 18:57, 15 September 2023 (UTC)
thread_title:  Doesn't answer the question "What is a spin structure"