Algebraic and Geometric Topology 5 (2005), paper no. 32, pages 751-768.

Bootstrapping in convergence groups

Eric L. Swenson

Abstract. 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 Lambda H 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.

Keywords. Convergence group, bootstrapping, Peano continuum

AMS subject classification. Primary: 20F32. Secondary: 57N10.

E-print: arXiv:math.GR/0508172

DOI: 10.2140/agt.2005.5.751

Submitted: 16 June 2004. Accepted: 24 June 2005. Published: 23 July 2005.

Notes on file formats

Eric L. Swenson
Mathematics Department, Brigham Young University
Provo, UT 84604, USA

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