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Bootstrapping in convergence groups

Eric L. Swenson
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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.

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Eric L. Swenson. 2005-08-09. Bootstrapping in convergence groups. https://doi.org/10.2140/agt.2005.5.751

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