Abstract

Let ?n (respectively, ??) be a free group of rank n (respectively, a free group of countable infinite rank). We consider the space of algebraic representations of the group ?n (respectively, ??) Hom(?n, PGL(2, C)) (respectively, Hom(?? PGL(2, C)) ). Inside each of these spaces we consider a couple of open and dense subsets. These subsets contain non-discrete groups of Möbius transformations. We proceed to find complex analytic parameters for these spaces given by fixed points.