Elementary intersection numbers on punctured spheres (Q1847614)

The author considers a \(2\)-sphere \(\Sigma_n\) with \(n\) punctures endowed with a hyperbolic metric. For \(n=4,5\) the author introduced projective coordinates for the space \(\mathcal{G}_n\) of simple closed geodesics on \(\Sigma_n\) in [Conform. Geom. Dyn. 1, 87-103 (1997; Zbl 0914.57008)] and [Ann. Acad. Sci. Fenn., Math. 26, 73-124 (2000; Zbl 1002.57038)]. The completion of these coordinates parametrize the space of all projective geodesic laminations. In this paper formulae for \(n \geq 5\) are presented for computing elementary intersection numbers generalizing results given in the papers cited above.