= Universal covering by the modular lambda function
{title2=$\lambda:\mathbb H\longrightarrow\mathbb C\setminus\{0,1\}$}
The <modular lambda function> is invariant under the projective level-two <principal congruence subgroup>. That group acts freely, and its quotient is the <level-two modular curve>. Adding its three <modular cusps> gives a sphere, and $\lambda$ has cusp values $0,1,\infty$, with simple orders in exponential cusp coordinates. Therefore it identifies the quotient with the sphere minus those three points. Since the <complex upper half-plane> is simply connected, this is a <universal covering map>, with the projective level-two group as its <deck transformation group>.
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