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Transactions of the American Mathematical Society

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Determining Thurston classes using Nielsen types

Author: Jane Gilman
Journal: Trans. Amer. Math. Soc. 272 (1982), 669-675
MSC: Primary 57N05; Secondary 30F99, 32G15, 57N05
MathSciNet review: 662059
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Abstract: In previous work [3] we showed how the Thurston or Bers classifications of diffeomorphisms of surfaces could be obtained using the Nielsen types of the lifts of the diffeomorphism to the unit disc. In this paper we find improved conditions on the Nielsen types for the Thurston and Bers classes. We use them to verify that an example studied by Nielsen is a pseudo-Anosov diffeomorphism with stretching factor of degree 4. This example is of interest in its own right, but it also serves to illustrate exactly how the Nielsen types are used for verifying examples. We discuss the general usefulness of this method.

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Keywords: Mapping-class group, Teichmüller modular group, Riemann surface, automorphism, pseudo-Anosov diffeomorphism, foliations, Fuchsian group
Article copyright: © Copyright 1982 American Mathematical Society

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