## Algebraic & Geometric Topology

### The bumping set and the characteristic submanifold

Genevieve S Walsh

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 14, Number 1 (2014), 283-297.

Dates
Revised: 31 May 2013
Accepted: 26 June 2013
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715801

Digital Object Identifier
doi:10.2140/agt.2014.14.283

Mathematical Reviews number (MathSciNet)
MR3158760

Zentralblatt MATH identifier
1279.30050

#### Citation

Walsh, Genevieve S. The bumping set and the characteristic submanifold. Algebr. Geom. Topol. 14 (2014), no. 1, 283--297. doi:10.2140/agt.2014.14.283. https://projecteuclid.org/euclid.agt/1513715801

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