complex of curves, mapping class group, surfaces

In this thesis, we study the automorphisms of a certain graph of nonseparating curvesand automorphisms of complexes of two-sided curves on surfaces. In Chapter 3, wedeal with the work of P. S. Schaller on mapping class groups of hyperbolic surfacesand automorphism groups of graphs for orientable surfaces of genus g ≥ 1 with npunctures. More precisely, it is shown that the automorphism group of the certaingraph is isomorphic to the extended mapping class group of the orientable surfaceproved by Schaller. In the last chapter of this thesis, we study the automorphisms ofthe complexes of two-sided simple closed curves on nonorientable surfaces of genusg with n holes.