  We present a study on how the outcomes of co-planar binary-single black hole
(BH) interactions distribute as a function of the orbital initial conditions.
We refer to this distribution as the topology. Using an $N$-body code that
includes BH finite sizes and gravitational wave (GW) emission in the
equation-of-motion (EOM), we perform more than a million three-body scatterings
to explore the topology of both the classical and the relativistic limit. We
further describe how the inclusion of GW emission in the EOM naturally leads to
scenarios where the binary-single system undergoes two successive GW mergers.
The time span from the first to the second GW merger is shortest in co-planar
interactions, and are for some configurations even short enough for LIGO to
observe both events. We note that co-planar interactions could be frequent in
environments such as active galactic nuclei discs.
