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Abstract
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We prove a true bootstrapping result for convergence groups acting
on a Peano continuum. We give an example of a Kleinian group
which is the
amalgamation of two closed hyperbolic surface groups along a simple closed curve. The limit
set is the
closure of a “tree of circles" (adjacent circles meeting in pairs of points). We alter the action
of on its limit
set such that
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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Keywords
convergence group, bootstrapping, Peano continuum
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Mathematical Subject Classification 2000
Primary: 20F34
Secondary: 57N10
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Publication
Received: 16 June 2004
Accepted: 24 June 2005
Published: 23 July 2005
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