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Teichmüller Spaces and the Rigidity of Mapping Class Group Actions

In: Surveys in Geometry I

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  • Ken’ichi Ohshika

    (Gakushuin University, Department of Mathematics, Faculty of Science)

Abstract

In this chapter, we survey the rigidity of mapping class group actions on Teichmüller spaces and curve complexes. We start from a classical result of Royden on the rigidity of the mapping class group action on Teichmüller space, together with its infinitesimal version. We then present Ivanov’s rigidity theorem on the mapping class group action on the curve complex, and show that this gives an alternative proof of Royden’s theorem. In the final part, we touch upon a recent result by Huang–Ohshika–Papadopoulos on the infinitesimal rigidity of the mapping class group action on Teichmüller space with Thurston’s asymmetric metric.

Suggested Citation

  • Ken’ichi Ohshika, 2022. "Teichmüller Spaces and the Rigidity of Mapping Class Group Actions," Springer Books, in: Athanase Papadopoulos (ed.), Surveys in Geometry I, chapter 0, pages 389-415, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-86695-2_10
    DOI: 10.1007/978-3-030-86695-2_10
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