Timeline for What is the significance of non-commutative geometry in mathematics?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Aug 7, 2023 at 4:39 | comment | added | plm | Dear @DavidCorfield, I am grateful to Mr Valette for leaving an answer here and regarding wikipedia i have the following comments to make: 1 In some languages like french the moderators/main editors of wiki are little tyrants and make it very unpleasant to try to contribute. So someone may have been deterred by that. 2 Some people just don't even know that wikipedia can be edited by anyone. 3 Some may feel uncomfortable with editing other ppl's work. After all it is quite unnatural in most situations in life: when you disagree with someone the reflex is to criticize, not change what he says. | |
| Dec 18, 2021 at 2:57 | comment | added | LSpice | Your link to the result of Guoliang Yu seems beyond the reach even of the Wayback Machine, so I used MathSciNet to search out the name of a likely paper. I hope that I got it correct. | |
| Dec 18, 2021 at 2:56 | history | edited | LSpice | CC BY-SA 4.0 |
Names of papers, and Wayback'd link, while this is on the front page
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| Feb 14, 2012 at 2:55 | comment | added | Ehsan M. Kermani | @Dear Alain: many thanks for your explanations. One of the reasons that I chose the Paul's answer is the sense that I got from the way he tried to relate important (classical) results that I've at least heard of many times to the known facts developed by NCG's method. As for my Q1, I'd say, unity of math sounds heroic and I don't really consider it as a motivation. | |
| Feb 11, 2012 at 14:46 | comment | added | David Corfield | "note that this Wikipedia entry rather stupidly says..." Why not edit it then? | |
| Feb 11, 2012 at 10:33 | comment | added | Yemon Choi | Alain, it has been a long time since I read about these things properly, and I am out of the office so cannot use MathSciNet to patch the gaps in my memory. Perhaps I will try to write something when I get back to the office. | |
| Feb 11, 2012 at 10:15 | comment | added | Alain Valette | @Yemon: Why don't you expand your relevant comment on Kaplansky-Kadison into a separate answer? | |
| Feb 11, 2012 at 9:25 | comment | added | Yemon Choi | I'd also put in a word for the Kadison-Kaplansky conjecture: in this case the problem originates in analysis rather than topology, but it seems that some of the most significant progress has either used NCG or used tools which received a lot of impetus from work in NCG | |
| Feb 11, 2012 at 8:56 | comment | added | Yemon Choi | Just as an addendum, and with caveat that AV can explain this better than I can. There's an article by Connes, late 80s or early 90s, where he mentions some of the work on the Novikov conjecture done using the early incarnations of the machinery mentioned. Unfortunately my copy is buried somewhere in my office, but I vaguely recall it used index theory for $C(T^n)=C*(Z^n)$ to give a proof of Novikov's conjecture for abelian groups, as motivation for the need to do differentiyal geometry on noncommutative spaces, viz. K-theory of C*-algebras, cyclic cohomology & Chern character, etc | |
| Feb 11, 2012 at 8:52 | comment | added | Amin | Cool, I didn't know about that ! | |
| Feb 11, 2012 at 8:49 | history | edited | Alain Valette | CC BY-SA 3.0 |
added 2 characters in body
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| Feb 11, 2012 at 8:41 | history | answered | Alain Valette | CC BY-SA 3.0 |