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The uniformization theorems of Riemann surfaces state that any Riemann surface can be constructed by an action of some group on some space. It is quite hard to find materials relating different ...

If $\mathcal{R}'$ is a closed subsurface of a hyperbolic surface $\mathcal{R}$, then there is an inclusion homomorphism between the mapping class groups: $$\text{Mod}(\mathcal{R}')\longrightarrow \...