12. Definition 2.6.3 - Cross Ratio

Let $z_{0}, z_{1}, z_{2}, z_{3} \in \hat{C}$ . Similar to what we saw in the previous proposition, we define the cross ratio of these three points as:
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q (z_{0}, z_{1}, z_{2}, z_{3}) = \frac{z_{0} - z_{1}}{z_{1} - z_{2}} \frac{z_{2} - z_{3}}{z_{3} - z_{0}}

Remark

The definition of the cross ratio is different in many textbooks but the main idea is the same.

Remark

By the previous proposition, we have that $q (f (z), w_{1}, w_{2}, w_{3}) = z$