Talk:Noncommutative geometry

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Mathematics rating:	Start Class	High Priority	Field: Geometry
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. At the moment, reads very much like a disambiguation page. Basically, one idea is regurgigated (lack of commutativity), but the article does not convey an accurate impression about either the goals or the methods of noncommutative geometry. Arcfrk 04:37, 15 June 2007 (UTC)

I don't entirely understand what the technical edit template is for in this case. The subject is very complicated, so the article is going to be technical if it is accurate. The adjectives are needed or the mentioned theorems may not work - I don't think we should try to get rid of them or describe them with "verbs", as every such adjective can be linked to an article explaining what it means. What I would push for is better exposition and more examples to motivate the topic. - Gauge 05:42, 3 September 2005 (UTC)

I agree with you, and feel that the article has come far enough that the template should be removed. One thing though, you should take a look at the article before the template was added. It was full of conversational sentences that were not appropriate, like: "What about the case of differential manifolds? Well...". The editing that you've done in your most recent edit, in my humble opinion, pushes this article over the edge so that it no longer has that 'needs editing' feel. - Tristanreid 20:41, 3 September 2005 (UTC)

Thank you. I will go ahead and remove the template then. - Gauge 23:58, 3 September 2005 (UTC)

[edit] Further Reading

I know Wikipedia isn't supposed to be a grocery list of references or whatever, but I feel that these resources are useful for people with the mathematical background of abstract algebra and differential geometry (speaking from experience...) so I wanted to share the papers:

• Noncommutative Geometry Year 2000 by Alain Connes

• Trace formula in noncommutative geometry and the zeros of the Riemann zeta function by Alain Connes

• A Short Survey of Noncommutative Geometry by Alain Connes

• Noncommutative finite-dimensional manifolds. I. Spherical manifolds and related examples by Alain Connes and Michel Dubois-Violette

• Non commutative finite dimensional manifolds II. Moduli space and structure of non commutative 3-spheres by Alain Connes and Michel Dubois-Violette

• SU(n)-Connections and Noncommutative Differential Geometry by Michel Dubois-Violette and Thierry Masson

• On Curvature in Noncommutative Geometry by M. Dubois-Violette, J. Madore, T. Masson, and J. Mourad

• Some aspects of noncommutative differential geometry by Michel Dubois-Violette

I found these useful for studying the subject, but others may not. Whatever. Pqnelson (talk) 00:53, 27 December 2007 (UTC)

Also, the quantum calculus dictionary which is defined by Connes has use of the Dixmier trace, which has few resources dedicated to it. I found this and a student studying this would find this to be an invaluable resource:

• Dixmier traces and some applications to noncommutative geometry by A.L. Carey and F. A. Sukochev

There is no wikipedia page on the Dixmier trace and I'm not sure if it deserves one, so I thought this may be a good alternative. Pqnelson (talk) 17:21, 28 December 2007 (UTC)