Determining Thurston classes using Nielsen types

Gilman, Jane

doi:10.1090/S0002-9947-1982-0662059-X

Determining Thurston classes using Nielsen types
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by Jane Gilman PDF

Trans. Amer. Math. Soc. 272 (1982), 669-675 Request permission

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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