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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Limits of limit sets, II: Geometrically infinite groups

Mahan Mj and Caroline Series

Geometry & Topology 21 (2017) 647–692
Abstract

We show that for a strongly convergent sequence of purely loxodromic finitely generated Kleinian groups with incompressible ends, Cannon–Thurston maps, viewed as maps from a fixed base limit set to the Riemann sphere, converge uniformly. For algebraically convergent sequences, we show that there exist examples where even pointwise convergence of Cannon–Thurston maps fails.

Keywords
Kleinian group, limit set, Cannon–Thurston map, geometrically infinite group
Mathematical Subject Classification 2010
Primary: 30F40, 57M50
References
Publication
Received: 13 June 2013
Revised: 7 June 2015
Accepted: 20 May 2016
Published: 17 March 2017
Proposed: Jean-Pierre Otal
Seconded: Bruce Kleiner, Martin Bridson
Authors
Mahan Mj
School of Mathematics
Tata Institute of Fundamental Research
Homi Bhabha Road
Mumbai 400005
India
http://www.math.tifr.res.in/~mahan
Caroline Series
Mathematics Institute
University of Warwick
Coventry
CV4 7AL
United Kingdom
http://www.maths.warwick.ac.uk/~masbb