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Realising end invariants by limits of minimally parabolic, geometrically finite groups

Ken'ichi Ohshika

Geometry & Topology 15 (2011) 827–890

DOI: 10.2140/gt.2011.15.827

Abstract

We shall show that for a given homeomorphism type and a set of end invariants (including the parabolic locus) with necessary topological conditions which a topologically tame Kleinian group with that homeomorphism type must satisfy, there is an algebraic limit of minimally parabolic, geometrically finite Kleinian groups which has exactly that homeomorphism type and the given end invariants. This shows that the Bers–Sullivan–Thurston density conjecture follows from Marden’s conjecture proved by Agol and Calegari–Gabai combined with Thurston’s uniformisation theorem and the ending lamination conjecture proved by Minsky, partially collaborating with Masur, Brock and Canary.

Keywords

Kleinian group, deformation space, end invariant, Bers–Sullivan–Thurston conjecture

Mathematical Subject Classification

Primary: 30F40, 57M50

References
Publication

Received: 15 January 2009
Revised: 11 March 2011
Accepted: 20 April 2011
Published: 8 June 2011
Proposed: David Gabai
Seconded: Jean-Pierre Otal, Danny Calegari

Authors
Ken'ichi Ohshika
Department of Mathematics
Graduate School of Science
Osaka University
Toyonaka
Osaka 560-0043
Japan