Abstract :

The mapping class group of a manifold is a group of all orientation-preserving diffeomorphisms up to isotopy. I will discuss mapping class group of some orientable surfaces. If time permits, I will discuss the idea of Lickorish twist theorem, which states that any orientation preserving homeomorphism of a closed orientable surface is generated by Dehn twists along 3g − 1 specific simple closed curves in the surface, where g denotes the genus of the surface.