Timeline for Why are local systems and representations of the fundamental group equivalent
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 1, 2017 at 17:37 | comment | added | Wenzhe | @DonuArapura Hi, Donu, I have a naive question about conventions. Since fundamental group acts on the right, should it be $f(x \gamma )=f(x) \rho (\gamma)$? Has the math community adopted the convection to write everything on the left when talking about things like monodromies? | |
| Mar 13, 2010 at 0:30 | comment | added | Donu Arapura | Yes, absolutely right. | |
| Mar 12, 2010 at 15:20 | comment | added | Ketil Tveiten | To give an alternative formulation of the same thing: One could consider the universal cover as a principal $\pi_1(X)$-bundle on X, then there exists a cover such that the transition functions $\gamma_{ij}$ (which are elements of $\pi_1$) of this bundle generate $\pi_1$, and one then gets transition functions on the associated bundle/local system by $\theta_{ij}:=\rho(\gamma_{ij})$. (I believe this works, but correct me if I'm wrong.) | |
| Mar 11, 2010 at 13:23 | history | edited | Donu Arapura | CC BY-SA 2.5 |
Slightly expanded.
|
| Mar 11, 2010 at 1:41 | history | answered | Donu Arapura | CC BY-SA 2.5 |