TFPT scientific source excerpt
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000135 | \subsection{Cross-Ratio as Unique Invariant}
000136 | 
000137 | Given four marked points $\{z_1, z_2, z_3, z_4\}$ on the boundary, the unique 
000138 | projective invariant is the cross-ratio:
000139 | \begin{equation}
000140 |     [z_1, z_2; z_3, z_4] = \frac{(z_1 - z_3)(z_2 - z_4)}{(z_1 - z_4)(z_2 - z_3)}
000141 | \end{equation}
000142 | 
000143 | \textbf{Consequence:} Any physical quantity depending only on boundary data must be 
000144 | expressible as a function of cross-ratios, hence as a M\"obius map.