On the geometric representation theory of discrete groups

First, the set of G-representations of a finitely generated group is described. This set of functions endowed with the compact-open topology will be used to prove some results in combinatorial group theory. Then we will see that the set of SL2( C )-representations may be viewed as an algebraic set. This new structure will allow some more applications in group theory. Finally, we will describe the set of characters of a finitely generated group and we will show that the set of characters associated to SL2( C )-representations also inherits an algebraic set structure