# Automorphisms of simple covers of Riemann surfaces

Can anybody give me a simple proof that simple covers of a Riemann surface have no covering automorphisms?

• What's a simple cover? A one-sheeted covering space? – jef808 May 7 '15 at 17:01
• it is a cover that has only simple branching, i.e. of type $z \mapsto z^2$ – IMeasy May 8 '15 at 9:16
• The example you wrote is a counterexample: $z \mapsto -z$ is a covering automorphism of $z \mapsto z^2$. – Lee Mosher May 8 '15 at 14:16