The bumping set and the characteristic submanifold

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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Keywords

Kleinian group, characteristic submanifold

Mathematical Subject Classification 2010

Primary: 30F40, 57M60

References

Publication

Received: 10 August 2012

Revised: 31 May 2013

Accepted: 26 June 2013

Preview posted: 5 December 2014

Published: 9 January 2014

Authors

Genevieve S Walsh
Department of Mathematics Tufts University 503 Boston Ave Medford, MA 02155 USA
http://www.tufts.edu/~gwalsh01/

Volume 14, issue 1 (2014)

Genevieve S Walsh

Abstract