Timeline for Kahler differentials and Ordinary Differentials
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 20, 2009 at 20:50 | comment | added | David E Speyer | I can't vote myself down, although I would if I could. I think my philosophy of voting is a little different from most users: my aim is to get the most useful answer to the top, and the less useful ones down, regardless of whether or not this is what the answer deserves in some moral sense. But, if you want to talk about voting strategies in detail, you should probably start a conversation at tea.mathoverflow.net. | |
| Nov 20, 2009 at 19:50 | comment | added | Georges Elencwajg | Dear David, I see some people (yourself maybe?!) have voted you down. This is ridiculous: I am voting you up ! | |
| Nov 20, 2009 at 7:42 | comment | added | Georges Elencwajg | Dear David, your gentlemanly reaction to my comment is incredibly gracious and generous. Let me use this opportunity to thank you and your colleagues for this (addictive!) wonderful site, whose lightning-fast success (1600 users in a little over a month) is more than deserved. | |
| Nov 20, 2009 at 6:01 | history | edited | David E Speyer | CC BY-SA 2.5 |
added 412 characters in body; added 57 characters in body
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| Nov 19, 2009 at 22:16 | comment | added | Georges Elencwajg | I think you are confusing me with Alberto (just below), since I didn't spend any time at all on constructions with local rings! MY post is the last one. It is perfectly true that 1-forms on M are, as you say, sums of global forms of the type fdg ( Kähler differentials surject on classical 1-forms as I mention in my post). The problem is, as you suggest yourself, that the equality of honest 1-forms cannot be proved just by linearity and Leibniz. To repeat my example, how would you prove in the case of M=R(the reals) that d(sin x)= (cos x)dx (true as one-forms) is true in the Kähler module ? | |
| Nov 19, 2009 at 20:41 | comment | added | David E Speyer | I think I'm right. I was a little confused by your answer because you spent a lot of time doing constructions with local rings, which I don't think you need to do. I'd be glad to hear about any error. Is it not true that any 1-form on a C^{\infty} manifold can be written as sum f_i d g_i, with f_i and g_i C^{infty} functions? I think this follows from the local fact and partitions of unity. Or am I wrong that two such expressions are equal if and only if their equality follows from the Liebnitz rule and linearity? Or is there some other error? | |
| Nov 19, 2009 at 17:58 | comment | added | Georges Elencwajg | Dear David, unless I misunderstand you I think the statements in the differentiable and holomorphic case are not quite correct. Would you care to have a look at my answer below? Friendly, | |
| Nov 19, 2009 at 14:07 | history | answered | David E Speyer | CC BY-SA 2.5 |