Teichmüller Spaces and the Rigidity of Mapping Class Group Actions

Ken’ichi Ohshika ()
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Ken’ichi Ohshika: Gakushuin University, Department of Mathematics, Faculty of Science

Chapter Chapter 10 in Surveys in Geometry I, 2022, pp 389-415 from Springer

Abstract: 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.

Keywords: Teichmüller space; Teichmüller metric; Thurston’s metric; Rigidity; Infinitesimal rigidity; Finsler structure; Mapping class group; Curve complex; 30F60; 57K20 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-86695-2_10

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DOI: 10.1007/978-3-030-86695-2_10

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