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A group $G$ acts on a compact Riemann surface $X$ if there is an injective homomorphism from $G$ to the group of automorphisms of $X$, i.e. a homomorphism $\phi: G \hookrightarrow \mathrm{Aut}(X)$.

Equivalently, a group $G$ acts on $X$ if there is a Fuchsian group $\Gamma$ and a surjective homomorphism $\eta: \Gamma \to G$ with $\ker( \eta)$ isomorphic to the fundamental group of $X$.

Knowl status:
  • Review status: beta
  • Last edited by Jennifer Paulhus on 2020-07-16 18:50:59
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