Cores of hyperbolic 3-manifolds and limits of Kleinian groups II

1999/03/12 by James W. Anderson, Anderson, James W., Richard D. Canary +1
Mathematics · #30F40 #57M50 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:30F40 #msc:57M50

paper · pdf · doi:10.48550/arxiv.math/9903076

To appear, Journal LMS

arxiv created 1999/03/12 · arxiv updated 2009/11/30

Abstract

Troels Jorgensen conjectured that the algebraic and geometric limits of an algebraically convergent sequence of isomorphic Kleinian groups agree if there are no new parabolics in the algebraic limit. We prove that this conjecture holds in 'most' cases. In particular, we show that it holds when the domain of discontinuity of the algebraic limit of such a sequence is non-empty. We further show, with the same assumptions, that the limit sets of the groups in the sequence converge to the limit set of the algebraic limit. As a corollary, we verify the conjecture for finitely generated Kleinian groups which are not (non-trivial) free products of surface groups and infinite cyclic groups.

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