| ¡@¡@According to Thurston, the set of all complete simple geodesics on a Riemann surface can be made into a topological space homeomorphic to a sphere whose dimension depends on the topology of the surface. By Thurston's result, the space $\overline{\cal G}_{n}$ of complete simple geodesics on an $n$-punctured sphere $\Sigma_{n}$ with $n \geq 4$ is homeomorphic to a sphere of dimension $2n-7$. ¡@¡@In this talk, a set of projective coordinates for $\overline{\cal G}_{n}$ with $n \leq 5$ will be given. We then describe how the results generalize to any $\Sigma_{n}$. |