Timeline for Kahler differentials and Ordinary Differentials
Current License: CC BY-SA 3.0
14 events
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| Apr 25, 2017 at 2:46 | history | edited | user13113 | CC BY-SA 3.0 |
deleted 3 characters in body
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| Nov 25, 2016 at 21:09 | comment | added | Fallen Apart | I do not understand why map $\Omega_k(A)\to\Omega^1(M)$ is surjective. Can you have a look at this MO.SE question? mathoverflow.net/questions/255601/… | |
| S Aug 30, 2016 at 12:57 | history | suggested | CommunityBot | CC BY-SA 3.0 |
Minor improvements to wording
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| Aug 30, 2016 at 12:45 | review | Suggested edits | |||
| S Aug 30, 2016 at 12:57 | |||||
| Apr 22, 2016 at 18:00 | comment | added | Denis Nardin | I'll mention that it is true that $\Omega^1(M)$ is the double dual of $\Omega_k(A)$. It follows from proposition 4.7 (vector fields are derivations on $C^\infty(M)$) and exercise 11-7 (tensor fields are $C^\infty(M)$-linear functions on $T(M)$) in Lee's smooth manifolds. | |
| Apr 22, 2016 at 17:53 | comment | added | Tyler Lawson | @Georges I understand that you may have strong feelings about the n-cafe, and you are entitled to them. However, I'm not sure that your comment addresses the issue. The mathematical content of Saal's question is whether the map $\Omega_k(A) \to \Omega^1(M)$ can be identified with the map $\Omega_k(A) \to \Omega_k(A)^{**}$, where $N^* = Hom_A(N,A)$ is the $A$-linear dual. This is not addressed by David Speyer's answer because perhaps every $A$-linear map $\Omega_k(A) \to A$ annihilates $d\sin(x) - \cos(x)dx$, by contrast with his construction $\Omega_k(A) \to K$ using an ultrafilter. | |
| Jan 2, 2016 at 9:09 | comment | added | Georges Elencwajg | @Saal No, it is not right. My experience with n-cafe is that whenever I look up a subject I find clear and elementary they will describe it in such abstract terms that I don't understand what they are talking about. Also, I've never seen them do any non-trivial calculations. But maybe they have done some: I no longer check their site which I find useless for me. But this is very personal. I guess some other mathematicians are enthusiastic about that site: more power to them. | |
| Jan 2, 2016 at 8:44 | comment | added | Saal Hardali | If I understood correctly the thread at $n$-cafe basically concludes with the ordinary de rham differentials being the double dual of kahler differentials. Is that right? | |
| Nov 20, 2009 at 19:19 | vote | accept | Abtan Massini | ||
| Nov 20, 2009 at 19:10 | vote | accept | Abtan Massini | ||
| Nov 20, 2009 at 19:19 | |||||
| Nov 19, 2009 at 20:40 | comment | added | Mariano Suárez-Álvarez | Georges is quite correct in that it is not trye that $d\mathrm{sin}=\mathrm{cos}dx$ in the module of Kähler differentials for $A$. | |
| Nov 19, 2009 at 20:36 | comment | added | Georges Elencwajg | Dear John, this is entirely possible. The definition I use is the same as in Weibel's book on Homological Algebra (8.8.1.),Qing Liu's (6.1.1.)and Hartshorne's (II,8) on Algebraic Geometry, Matsumura's on Commutative Ring Theory (9.25),Bourbaki's Algebra ( III,$10,11) and actually in all the books on the subject that I know of. What other definition of Kähler differentials do you have in mind? Greetings, | |
| Nov 19, 2009 at 19:49 | comment | added | John McCarthy | I think your definition of Kahler differentials differs from that in the other two entries. | |
| Nov 19, 2009 at 17:24 | history | answered | Georges Elencwajg | CC BY-SA 2.5 |