| Let be the set of all simple closed geodesics on a four punctured sphere According to Thurston, the set of all simple geodesics on can be made into a topological space homeomorphic to a circle so that is dense in . In this lecture, I shall talk about how to construct an explicit homeomorphism of onto by using geometric intersection numbers which can be read off easily from the geometry of geodesics. Also, if time is permitted, I shall talk about my recent work along this line on a five punctured sphere. |