Determining thurston classes using nielsen types

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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 hits 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.

Original languageEnglish (US)
Pages (from-to)669-675
Number of pages7
JournalTransactions of the American Mathematical Society
Issue number2
StatePublished - Aug 1982

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


  • Automor­phism
  • Foliations
  • Fuchsian group
  • Mapping-class group
  • Pseudo-anosov diffeomorphism
  • Riemann surface
  • Teichmüller modular group

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