Timeline for The "miracle" of Heegard Floer.
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 3, 2009 at 2:04 | vote | accept | Max M | ||
| Nov 3, 2009 at 2:03 | comment | added | Max M | I think you are right. I was hoping to get some info on the gauge theory. From what I gather, the idea is that the symmetric product is the space of solutions of vortex equations - explained arxiv.org/abs/math/0606063 This is U(1) gauge theory,and presumably "monopole" version of Atiyah-Floer is what produces the Heegard Floer, which Ozsvath-Szabo then went on to study directly. I wonder if anyone can flesh out some details (e.g. how to the Lagrangian tori arise). | |
| Nov 2, 2009 at 21:20 | comment | added | Ben Webster♦ | I think it's a caricature of their thought processes. This TQFT is supposed to come from gauge theory which was known at the time. In particular, I believe that the symmetric power showed as a space of some solutions to equations. I would say the point of that work of Auroux is that you can explicitly reconstruct the higher levels of the TQFT from the Heegard Floer theory. | |
| Nov 2, 2009 at 20:58 | comment | added | Max M | Yes, of course. Denis Auroux gave a talk about it www-math.mit.edu/~auroux/papers/slides-fuksymg.pdf and it does remove the miraculousness. But this was a posteriori, in light of Lipshitz-Ozsvath-Thurston. Surely this is not how Ozsváth-Szabo came up with this? | |
| Nov 2, 2009 at 19:54 | history | answered | Ben Webster♦ | CC BY-SA 2.5 |