Volume 14, issue 1 (2014)

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The bumping set and the characteristic submanifold

Genevieve S Walsh

Algebraic & Geometric Topology 14 (2014) 283–297
Abstract

We show here that the Nielsen core of the bumping set of the domain of discontinuity of a Kleinian group $\Gamma$ is the boundary of the characteristic submanifold of the associated $3$–manifold with boundary. Some examples of interesting characteristic submanifolds are given. We also give a construction of the characteristic submanifold directly from the Nielsen core of the bumping set. The proofs are from “first principles”, using properties of uniform domains and the fact that quasi-conformal discs are uniform domains.

Keywords
Kleinian group, characteristic submanifold
Mathematical Subject Classification 2010
Primary: 30F40, 57M60