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$\begingroup$ 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.) $\endgroup$

Ketil Tveiten
– Ketil Tveiten

2010-03-12 15:20:56 +00:00
Commented Mar 12, 2010 at 15:20
$\begingroup$ Yes, absolutely right. $\endgroup$

Donu Arapura
– Donu Arapura

2010-03-13 00:30:15 +00:00
Commented Mar 13, 2010 at 0:30
$\begingroup$ @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? $\endgroup$

Wenzhe
– Wenzhe

2017-03-01 17:37:13 +00:00
Commented Mar 1, 2017 at 17:37

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