Timeline for Has Witten's perturbation on de Rham complex been studied on other elliptic complexes?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 5 at 19:48 | answer | added | Ben McKay | timeline score: 2 | |
| May 5 at 17:56 | answer | added | Gibbon | timeline score: 3 | |
| Aug 28, 2014 at 17:53 | comment | added | Steven Gubkin | Would also like to note that $d_h (f) = e^{-h} d( e^h f) = e^{-h} (e^h df + e^h dh \wedge f ) = df+dh \wedge f$. So we have $d_h = d + dh \wedge$, which is a flat connection on the trivial bundle. So that is another set of keywords to search for when thinking about this stuff. | |
| Jan 15, 2014 at 22:31 | answer | added | Steven Gubkin | timeline score: 12 | |
| Jan 15, 2014 at 21:34 | answer | added | Peter Samuelson | timeline score: 1 | |
| Jan 15, 2014 at 10:19 | comment | added | j.c. | I'm not sure if this is what you're asking but I believe this is the idea behind the supersymmetric proofs of the Atiyah-Singer index theorem. I'm in no position to explain the details though. | |
| Jan 15, 2014 at 0:43 | comment | added | Vesselin Dimitrov | Also, regarding the Dolbeault complex, Demailly's "Champs magnetiques et inegalites de Morse pour la $d''$-cohomologie" was largely inspired by Witten's technique. | |
| Jan 15, 2014 at 0:26 | comment | added | Vesselin Dimitrov | A twisting of the Dolbeault complex is required for the proof of Ohsawa and Takegoshi's famous holomorphic extension theorem. See section 2 in J.-P. Demailly's account, "On the Ohsawa-Takegoshi-Manivel $L^2$-existence theorem." | |
| Jan 14, 2014 at 22:48 | history | asked | Asghar Ghorbanpour | CC BY-SA 3.0 |