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The core chain of circles of Maskit's embedding for once-punctured torus groups


Author: Irene Scorza
Journal: Conform. Geom. Dyn. 10 (2006), 288-325
MSC (2000): Primary 30F40; Secondary 57M50
DOI: https://doi.org/10.1090/S1088-4173-06-00134-2
Published electronically: October 10, 2006
MathSciNet review: 2261053
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Abstract: In this paper, we describe the limit set $ \Lambda_n$ of a sequence of manifolds $ N_n$ in the boundary of Maskit's embedding of the once-punctured torus. We prove that $ \Lambda_n$ contains a chain of tangent circles $ \{C_{n,j}\}$ that are described from the end invariants of the manifold. In particular, we give estimates in terms of $ n$ of the radii $ r_{n,j}$ of the circles and prove that $ r_{n,j}$ decrease when $ n$ tends to infinity. We then apply these results to McShane's identity, to obtain an estimate of the width of the limit set in terms of $ n$.


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Additional Information

Irene Scorza
Affiliation: Dipartimento di Matematica, Università di Genova, Via Dodecaneso, 35 - 16146 Genova, Italy
Email: scorza@dima.unige.it

DOI: https://doi.org/10.1090/S1088-4173-06-00134-2
Keywords: Kleinian groups, limit sets.
Received by editor(s): January 19, 2005
Published electronically: October 10, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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