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arXiv · 1208.1700

The bumping set and the characteristic submanifold

Genevieve S. Walsh
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Abstract

We show here that the Nielsen core of the bumping set of the domain of discontinuity of a Kleinian group $Γ$ 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.

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Genevieve S. Walsh. 2012-09-18. The bumping set and the characteristic submanifold. https://doi.org/10.2140/agt.2014.14.283

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