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2005 Bootstrapping in convergence groups
Eric L Swenson
Algebr. Geom. Topol. 5(2): 751-768 (2005). DOI: 10.2140/agt.2005.5.751


We prove a true bootstrapping result for convergence groups acting on a Peano continuum. We give an example of a Kleinian group H which is the amalgamation of two closed hyperbolic surface groups along a simple closed curve. The limit set ΛH is the closure of a “tree of circles" (adjacent circles meeting in pairs of points). We alter the action of H on its limit set such that H no longer acts as a convergence group, but the stabilizers of the circles remain unchanged, as does the action of a circle stabilizer on said circle. This is done by first separating the circles and then gluing them together backwards.


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Eric L Swenson. "Bootstrapping in convergence groups." Algebr. Geom. Topol. 5 (2) 751 - 768, 2005.


Received: 16 June 2004; Accepted: 24 June 2005; Published: 2005
First available in Project Euclid: 20 December 2017

zbMATH: 1083.20039
MathSciNet: MR2153108
Digital Object Identifier: 10.2140/agt.2005.5.751

Primary: 20F34
Secondary: 57N10

Keywords: Bootstrapping , convergence group , Peano continuum

Rights: Copyright © 2005 Mathematical Sciences Publishers


Vol.5 • No. 2 • 2005
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