Abstract:
The mapping class group of an orientable surface of genus g is the group of all orientation preserving piecewise linear homeomorphisms of the surface up to isotopy. In this thesis it is shown that the mapping class group of an orientable surface of genus g is generated by Dehn twists about nonseparating simple closed curves [15]. Then the notion of cohomology groups of a group is introduced following [18]. The first cohomology groups of the mapping class groups of orientable surfaces of genus g greater than one are shown to be trivial [16].
