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

Scorza, Irene

doi:10.1090/S1088-4173-06-00134-2

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 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 of the radii $r_{n,j}$ of the circles and prove that $r_{n,j}$ decrease when 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 .

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