Relatively hyperbolic groups with planar boundaries

In this article, we prove a version of Martin and Skora's conjecture that convergence groups on the 2-sphere are covered by Kleinian groups. Given a relatively hyperbolic group pair (G, P) with planar boundary and no Sierpinski carpet or cut points in its boundary, and with G one ended and virtually having no 2-torsion, we show that G is virtually Kleinian. We also give applications to various versions of the Cannon conjecture and to convergence groups acting on S².