Timeline for Floer homology and Invariants for Einstein Field Equations?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 7, 2017 at 20:53 | comment | added | user100272 | @RobertHaslhofer Donaldson's proposal, I understand it, is not to count have a gauge theory counting associative submanifolds but to have a gauge theory counting G$_2$ instantons, arrising from a certain G$_2$ functional. But it turns out that G$_2$ instantons can bubble out of associative $3$-folds and so such a gauge theory needs to keep track of associative $3$-folds. | |
| Nov 11, 2012 at 23:24 | comment | added | Robert Haslhofer | @Chris: Ricci-flat metrics are critical points but never extrema of the Einstein-Hilbert functional. You can see this from the formula for the second variation, which has a different sign (at the level of the symbol!) in conformal and in TT directions, i.e. there are always infinitely many positive and infinitely many negative directions. In Perelman's lambda-functional there is a minimization over all densities (this roughly corresponds to the conformal directions), which kills all the positive directions (except possibly finitely many), so you get extrema and the gradient flow makes sense. | |
| Nov 10, 2012 at 18:02 | vote | accept | Chris Gerig | ||
| Nov 9, 2012 at 3:04 | comment | added | Chris Gerig | Could you elaborate a little on your point#2? | |
| Aug 23, 2012 at 16:14 | comment | added | Deane Yang | Thanks! I had forgotten about the special holonomy equations. They do indeed appear to be the analogue of self-dual connections. | |
| Aug 23, 2012 at 16:03 | history | answered | Robert Haslhofer | CC BY-SA 3.0 |