Mapping Class Groups

  • Sang-hyun Kim
  • Thomas Koberda
  • Mahan Mj
Part of the Lecture Notes in Mathematics book series (LNM, volume 2231)


In this chapter, we shift the focus to exotic actions of mapping class groups on the circle, where here “exotic” means “not conjugate to Nielsen’s standard action” (see Handel and Thurston (Adv Math 56:173–191, 1985) and Casson and Bleiler (Automorphisms of Surfaces After Nielsen and Thurston, Cambridge University Press, Cambridge, 1988) for detailed discussions of Nielsen’s action). We first discuss actions of fibered, hyperbolic 3-manifold groups on S1, in relation to Nielsen’s action.


  1. 16.
    B.H. Bowditch, M. Sakuma, The action of the mapping class group on the space of geodesic rays of a punctured hyperbolic surface. Groups Geom. Dyn. 12(2), 703–719 (2018). MR 3813207MathSciNetCrossRefGoogle Scholar
  2. 25.
    D. Calegari, Universal circles for quasigeodesic flows. Geom. Topol. 10, 2271–2298 (2006) (electronic). MR 2284058MathSciNetCrossRefGoogle Scholar
  3. 27.
    D. Calegari, N.M. Dunfield, Laminations and groups of homeomorphisms of the circle. Invent. Math. 152(1), 149–204 (2003). MR 1965363 (2005a:57013)Google Scholar
  4. 48.
    É. Ghys, Groups acting on the circle. Enseign. Math. (2) 47(3–4), 329–407 (2001). MR 1876932 (2003a:37032)Google Scholar
  5. 59.
    K. Honda, W.H. Kazez, G. Matić, Right-veering diffeomorphisms of compact surfaces with boundary. Invent. Math. 169(2), 427–449 (2007). MR 2318562MathSciNetCrossRefGoogle Scholar
  6. 97.
    H. Short, B. Wiest, Orderings of mapping class groups after Thurston. Enseign. Math. (2) 46(3–4), 279–312 (2000). MR 1805402Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Sang-hyun Kim
    • 1
  • Thomas Koberda
    • 2
  • Mahan Mj
    • 3
  1. 1.School of MathematicsKorea Institute for Advanced StudySeoulRepublic of Korea
  2. 2.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA
  3. 3.School of MathematicsTata Institute of Fundamental ResearchMumbaiIndia

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