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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



Pleating coordinates for the Teichmüller space of a punctured torus

Authors: Linda Keen and Caroline Series
Journal: Bull. Amer. Math. Soc. 26 (1992), 141-146
MSC (2000): Primary 30F40; Secondary 30F60, 32G15, 57N05, 57S30
MathSciNet review: 1110439
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Abstract: We construct new coordinates for the Teichmüller space Teich of a punctured torus into $ {\text{R}} \times {{\text{R}}^ + }$. The coordinates depend on the representation of Teich as a space of marked Kleinian groups $ {G_\mu }$ that depend holomorphically on a parameter $ \mu $ varying in a simply connected domain in C. They describe the geometry of the hyperbolic manifold $ {{\text{H}}^3}{\text{/}}{G_\mu }$; they reflect exactly the visual patterns one sees in the limit sets of the groups $ {G_\mu }$; and they are directly computable from the generators of $ {G_\mu }$.

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Article copyright: © Copyright 1992 American Mathematical Society