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On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces

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References

  1. Abikoff, W., Degenerating families of Riemann surfaces.Ann. of Math., 105 (1977), 29–44.

    Article  MATH  MathSciNet  Google Scholar 

  2. Abikoff, W.,The Real Analytic Theory of Techmüller Spaces. Springer Lecture Notes in Mathematics, 820 (1980).

  3. Ahlfors, L. V., On quasiconformal mappings.J. Analyse Math., 3 (1953/4), 1–58.

    Article  MathSciNet  Google Scholar 

  4. Baer, R., Kurventypen auf Flächen.J. Reine Angew. Math., 156 (1927), 231–246.

    MATH  Google Scholar 

  5. —, Isotopie von Kurven auf orientierbaren, geschlossernen Flachen und ihr Zusammenhang mit der topologischen Deformation der Flachen.J. Reine Angew. Math., 159. (1928), 101–111.

    MATH  Google Scholar 

  6. Bers, L., On boundaries of Teichmüller spaces and on Kleinian groups: I.Ann. of Math., 91 (1970), 570–600.

    Article  MATH  MathSciNet  Google Scholar 

  7. —, Extremal quasiconformal mappings, Advances in the theory of Riemann surfaces.Ann. of Math. Studies, 66 (1971), 27–52.

    MathSciNet  Google Scholar 

  8. —, Fiber spaces over Teichmüller spaces.Acta Math., 130 (1973), 89–126.

    Article  MATH  MathSciNet  Google Scholar 

  9. —, An extremal problem for quasiconformal mappings and a theorem by Thurston.Acta Math., 141 (1978), 73–98.

    MATH  MathSciNet  Google Scholar 

  10. —, The action of the modular group on the complex boundary, Riemann surfaces and related topics.Ann. of Math. Studies, 97 (1980), 33–52.

    MathSciNet  Google Scholar 

  11. Birman, J. S., The algebraic structure of surface mapping class group: Chapter 6 ofDiscrete Groups and Automorphic Functions. Edited by W. J. Harvey, Academic Press, London, 1977, 163–198.

    Google Scholar 

  12. Earle, C. J., On holomorphic cross sections in Teichmüller spaces.Duke Math. J., 36 (1969), 409–416.

    Article  MATH  MathSciNet  Google Scholar 

  13. Earle, C. J. &Kra, I., On holomophic mappings between Teichmüller spaces, inContributions to Analysis. Edited by L. V. Ahlfors, et al., Academic Press, New York, 1974, 107–124.

    Google Scholar 

  14. Epstein, D. B. A., Curves on 2-manifolds and isotopies.Acta Math., 115 (1966), 83–107.

    Article  MATH  MathSciNet  Google Scholar 

  15. Farkas, H. M. &Kra, I.,Riemann Surfaces, Springer-Verlag, New York and Berlin, 1980.

    MATH  Google Scholar 

  16. Gardiner, F. P., Schiffer's interior variation and quasiconformal mapping.Duke Math. J., 42 (1975), 371–380.

    Article  MATH  MathSciNet  Google Scholar 

  17. Gehring, F. W., Quasiconformal mappings which hold the real axis pointwise fixed, inMathematical Essays dedicated to A. J. Macintyne, Ohio Univ. Press, Athens, Ohio, 1970, 145–148.

    Google Scholar 

  18. Gilman, J., On the Nielsen type and the classification for the mapping-class group. To appear.

  19. Kerckhoff, S. P., The asymptotic geometry of Teichmüller space.Topology, 19 (1980), 23–41.

    Article  MATH  MathSciNet  Google Scholar 

  20. —, The Nielsen realization problem.Bull. Amer. Math. Soc., 2 (1980), 452–454.

    Article  MATH  MathSciNet  Google Scholar 

  21. Kra, I.,Automorphic forms and Kleinian groups. Benjamin, Reading, Massachusetts, 1972.

    MATH  Google Scholar 

  22. — On new kinds of Teichmüller spaces.Israel J. Math., 16 (1973), 237–257.

    MathSciNet  Google Scholar 

  23. —, On Teichmüller's theorem on the quasi-invariance of the cross ratios.Israel J. Math., 30 (1978), 152–158.

    MATH  MathSciNet  Google Scholar 

  24. Kra, I., Canonical mappings between Teichmüller spaces.Bull. Amer. Math. Soc. To appear.

  25. Kravetz, S., On the geometry of Teichmüller spaces and the structure of their modular groups.Ann. Acad. Sci. Fenn., 278 (1959), 1–35.

    MathSciNet  Google Scholar 

  26. Marden, A. &Masur, H., A foliation of Teichmüller space by twist invariant discs.Math. Scand., 36 (1975), 211–228 and Addendum, 39 (1976), 232–238.

    MATH  MathSciNet  Google Scholar 

  27. Maskit, B. & Matelski, J. P., Minimal geodesics on surfaces. To appear.

  28. Matelski, J. P., A compactness theorem for Fuchsian groups of the second kind.Duke Math. J., 43 (1976), 829–840.

    Article  MATH  MathSciNet  Google Scholar 

  29. Nag, S., Non-geodesic discs embedded in Teichmüller spaces. To appear.

  30. Nielsen, J., Untersuchungen zur Topologie der geschlossenen zweiseitigen Flachen.Acta Math., 50 (1927), 189–358; 53 (1929), 1–76; and 58 (1932), 87–167.

    Article  MATH  MathSciNet  Google Scholar 

  31. Poénaru, V., Travaux de Thurston sur les diffeomorphismes des surfaces et l'espace de Teichmüller.Sem. Bourbaki, 529 (1978/79).

  32. Poénaru, V. et al., Travaux de Thurston sur les surfaces.Asterisque, 66–67 (1979).

  33. Riera, G., Semi-direct products of Fuchsian groups and uniformization.Duke Math. J., 44 (1977), 291–304.

    Article  MATH  MathSciNet  Google Scholar 

  34. Royden, H. L., Automorphisms and isometries of Techmüller space, Advances in the theory of Riemann surfaces.Ann. of Math. Studies, 66 (1971), 369–383.

    MathSciNet  Google Scholar 

  35. Teichmüller, O., Ein Verschiebungssatz der quasikonformen Abbildung.Deutsche Math., 7 (1942), 336–343.

    Google Scholar 

  36. Thurston, W. P., On the geometry and dynamics of diffeomorphisms of surfaces. To appear.

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Research partially supported by NSF Grant MCS 7801248.

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Kra, I. On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces. Acta Math 146, 231–270 (1981). https://doi.org/10.1007/BF02392465

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  • DOI: https://doi.org/10.1007/BF02392465

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