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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