Torelli group in dimension two

In this talk, I will talk about the Torelli group of an orientable surface which is the subgroup of the mapping class group consisting of elements which act trivially on the homology. We will see that this group surjects onto Sp(2g,Z), and with the help of this surjection, how Birman, Powell and Johnson found generating sets for the Torelli group. Then, I will talk about the minimality of the Humphries' generating set of Dehn twists.