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We show here that the Nielsen core of the bumping set of the domain ofdiscontinuity of a Kleinian group $\Gamma$ is the boundary of thecharacteristic submanifold of the associated 3-manifold with boundary. Someexamples of interesting characteristic submanifolds are given. We also give aconstruction of the characteristic submanifold directly from the Nielsen coreof the bumping set. The proofs are from "first principles", using properties ofuniform domains and the fact that quasi-conformal discs are uniform domains.

The bumping set and the characteristic submanifold