Timeline for Is a non-flat hermitian connection determined uniquely by its holonomy and curvature?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 4, 2016 at 19:45 | vote | accept | David Roberts | ||
| Mar 4, 2016 at 13:30 | comment | added | user21574 | @Sebastian Goette, thank you , good comment | |
| Mar 4, 2016 at 10:56 | comment | added | Sebastian Goette | The procedure sketched in the first paragraph gives a solution, but only up to a possible twist by a flat line bundle. To detect this, instead of $\alpha$ (which is well-defined only if the connection is flat), you need to specify the holonomy along a fixed set of loops generating $H_1(M)$. Remember on one hand that holonomy is gauge invariant, hence well-defined in our context. On the other hand, if the curvature is nonzero, you can always choose a representative of each class in $\pi_1(M)$ such that you obtain any prescribed value for the holonomy. | |
| Mar 4, 2016 at 9:43 | history | answered | Tobias Diez | CC BY-SA 3.0 |