Primitive-stable and Bowditch actions on hyperbolic spaces

In this talk, we will introduce Bowditch representations of the free group of rank two (defined by Bowditch in 1998) along with primitive-stable representations (defined by Minsky in 2010) acting on Gromov hyperbolic spaces. Minsky first introduced primitive-stable representations in PSL(2,C) to construct an open domain of discontinuity in the character variety. We will discuss the equivalence between primitive-stable and Bowditch representations. We will also introduced simple-stable representations of a surface group and give a similar result in the case of the four-punctured sphere.