On the Maskit Slice of 4-dimensional Kleinian Punctured Torus Groups

Let Γ be a 3-dimensional Kleinian punctured torus group with accidental parabolics. The deformation space of Γ in the group of Möbius transformations on the 2-sphere is well-known as the Maskit slice of punctured torus groups. In this paper, we study the deformation space of Γ in the group of Möbius transformations on the 3-sphere, where Γ is naturally regarded as a 4-dimensional Kleinian group. We will show that this space is realized as a domain of 3-space R, which contains the original Maskit slice as a slice through a plane. Furthermore, we will show that the space also contains the Maskit slice of fourth-punctured sphere groups as a slice through another plane. Some of another slices of the space will be also studied.