The planar Bowditch boundary conjecture for relatively hyperbolic groups

Let $(G,\mathcal{P})$ be a relatively hyperbolic group pair, with Bowditch boundary $\partial(G,\mathcal{P})$. A boundary is planar if it embeds in the plane, and it has no cut points if deleting any single point leaves it connected. The planar Bowditch boundary conjecture. If $\partial(G,\mathcal{P})$ is planar and has no cut points, then $G$ is virtually a geometrically finite Kleinian group. This gives sufficient conditions for a relatively hyperbolic group to be virtually a geometrically finite Kleinian group; planarity is necessary, while the role of cut points is subtle because geometrically finite Kleinian groups can have Bowditch boundaries with cut points. The conjecture is attributed in the source to work cited as HW1, and its resolution is not specified here.