#### 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

Email: eric@math.byu.edu

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