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On discreteness of Mobius groups

Xi Fu
대한수학회 (The Korean Mathematical Society)|2013.05|대한수학회보 (Bulletin of the KMS)|제50권 제3호|pp. 747-752

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참고문헌

키워드

discretenesselliptic elementsloxodromic elements
주제분류수학

초록

It’s known that one could use a fixed loxodromic or parabolic element in M(Rn) as a test map to test the discreteness of a nonelementary M¨obius group G. In this paper, we discuss the discreteness of G by using a fixed elliptic element.

Abstract

It’s known that one could use a fixed loxodromic or parabolic element in M(Rn) as a test map to test the discreteness of a nonelementary M¨obius group G. In this paper, we discuss the discreteness of G by using a fixed elliptic element.

참고문헌 (13)

  1. A. F. Beardon, "The Geometry of discrete groups, Graduate text in Mathematics, Vol. 91" (1983), Springer-Verlag
  2. W. Cao, "Discreteness criteria and algebraic convergence theorem for subgroups in PU(1, n;C)", Proc. Japan Acad. Ser. A Math. Sci, 82(3), pp.49~52 (2006)
  3. S. S. Chen, "Hyperbolic spaces, Contributions to analysis (a collection of papers dedicated to Lipman Bers)", pp.49~87 (1974), Academic Press
  4. T. Jørgensen, "On discrete groups of M¨obius transformation", Amer. J. Math, 98(3), pp.739~749 (1976)
  5. T. Jørgensen, "A note on subgroups of SL(2,C)", Quart. J. Math. Oxford Ser, 28(110), pp.209~211 (1977)
  6. L. Li, "Elliptic elements in Mobius groups", Proc. Japan Acad. Ser. A Math. Sci, 86(3), pp.69~72 (2010)
  7. Liulan Li, "DISCRETENESS BY USE OF A TEST MAP", 대한수학회보, 49(1), pp.57~61 (2012), 대한수학회
  8. P. Tukia, "Discreteness of subgroups of SL(2, C) containing elliptic elements", Math. Scand, 91(2), pp.214~220 (2002)
  9. X. Wang, "Dense subgroups of n-dimensional Mobius groups", Math. Z, 243(4), pp.643~651 (2003)
  10. X. Wang, "Discreteness criteria for M¨obius groups acting on M(Rn)", Israel J. Math, 150, pp.357~368 (2005)
  11. X. Wang, "Discreteness criterions for subgroups in SL(2,C)", Math. Proc. Cambridge Philos. Soc, 124(1), pp.51~55 (1998)
  12. X. Wang, "Discreteness criteria of M¨obius groups of high dimensions and convergence theorems of Kleinian groups", Adv. Math, 159(1), pp.68~82 (2001)
  13. P. Waterman, "Mobius transformations in several dimensions", Adv. Math, 101(1), pp.87~113 (1993)

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