The bumping set and the characteristic submanifold

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.

12 pages, 2 figures; non-mathematical error fixed (The author's name is now on the title page.)

References in corpus (1)

• Hyperbolic Structures on 3-manifolds, III: Deformations of 3-manifolds with incompressible boundary

Cited by in corpus (1)

• Quasi-isometric rigidity of three manifold groups