Limits of limit sets, II: Geometrically infinite groups

Mj, Mahan; Series, Caroline

doi:10.2140/gt.2017.21.647

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Limits of limit sets, II: Geometrically infinite groups

Mahan Mj and Caroline Series

Geometry & Topology 21 (2017) 647–692

DOI: 10.2140/gt.2017.21.647

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

Volume 21, issue 2 (2017)