Timeline for Proving Hodge decomposition without using the theory of elliptic operators?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Jun 16, 2010 at 17:19 | vote | accept | Konrad Voelkel | ||
| Jun 16, 2010 at 17:19 | comment | added | Konrad Voelkel | Thank you for the reference to Lange and Birkenhake, I didn't know this book. It is exactly what I was looking for: a class of Kähler manifolds where we are able to prove Hodge decomposition more easily. This example might be useful to see more directly what's going on (in the proof). | |
| Jun 15, 2010 at 22:15 | comment | added | Tim Perutz | Moreover, studying tori isn't a diversion from the general case; the Sobolev theory can be done neatly on tori using Fourier series, and then transplanted to other manifolds. This is the line taken by Griffiths & Harris, who I think give a very good account of the Hodge theorem. Wells sets things up in the generality needed by Atiyah-Singer - for Hodge theory, this is overkill. | |
| Jun 15, 2010 at 19:52 | history | answered | Andy Putman | CC BY-SA 2.5 |