Classical two-parabolicT-Schottky Groups

AT-Schottky group is a discrete group of Möbius transformations whose generators identify pairs of possibly-tangent Jordan curves on the complex sphere ?. If the curves are Euclidean circles, then the group is termed classicalT-Schottky. We describe the boundary of the space of classicalT-Schottky groups affording two parabolic generators within the larger parameter space of allT-Schottky groups with two parabolic generators. This boundary is surprisingly different from that of the larger space. It is analytic, while the boundary of the larger space appears to be fractal. Approaching the boundary of the smaller space does not correspond to pinching; circles necessarily become tangent, but extra parabolics need not develop. As an application, we construct an explicit one parameter family of two parabolic generator non-classicalT-Schottky groups.