Moduli space of Riemann surfaces
= Moduli space of Riemann surfaces
{title2=$\mathcal M_g$}
= Moduli spaces of Riemann surfaces
{synonym}
= Riemann surface moduli space
{c}
{synonym}
The <moduli space> of unmarked <compact> <genus>-$g$ <Riemann surfaces>. For $g\geq2$ it is the quotient $\mathcal T_g/\operatorname{Mod}(S_g)$ of <Teichmüller space> by the <mapping class group>, with its quotient topology. The thick subsets are <compact> by <Mumford's compactness theorem>.