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Convergence groups are Fuchsian groups


Author: David Gabai
Journal: Bull. Amer. Math. Soc. 25 (1991), 395-402
MSC (1985): Primary 57S25; Secondary 20H10, 57N05, 57N10
DOI: https://doi.org/10.1090/S0273-0979-1991-16082-9
MathSciNet review: 1102752
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  • [E] D. B. A. Epstein, Periodic flows on 3-manifolds, Ann. of Math. (2) 95 (1972), 66-82. MR 288785
  • [F1] C. D. Feustel, On the Torus theorem and its applications, Trans. Amer. Math. Soc. 217 (1976), 1-43. MR 394666
  • [F2] C. D. Feustel, On the torus theorem for closed 3-manifolds, Trans. Amer. Math. Soc. 217 (1976), 45-57. MR 394667
  • [G] D. Gabai, Convergence groups are Fuchsian groups, preprint. MR 1189862
  • [GH] C. Gordon and W. Heil, Cyclic normal subgroups of fundamental groups of 3-manifolds, Topology 14 (1975), 305-309. MR 400232
  • [GM] F. W. Gehring and G. Martin, Discrete quasiconformal groups I, Proc. London Math. Soc. (3) 55 (1987), 331-358. MR 896224
  • [J] K. Johannson, Homotopy equivalences of 3-manifolds with boundary, Lecture Notes in Math., vol. 761, Springer-Verlag, Berlin and New York, 1979. MR 551744
  • [JS] W. H. Jaco and P. B. Shalen, Seifert fibered spaces in 3-manifolds, Mem. Amer. Math. Soc. 2 (1979). MR 539411
  • [K] S. P. Kerckhoff, The Nielsen realization problem, Ann. of Math. (2) 117 (1983), 235-265. MR 690845
  • [Kn] H. Kneser, Gerschlossene Flachen in dreidimensionalen Mannigfaltigkeiten, Jahres. der Deut. Math. Verein. 38 (1929), 248-260.
  • [M] G. Mess, The Seifert conjecture and groups which are coarse quasi isometric to planes, preprint.
  • [Mi] J. Milnor, A unique factorization theorem for 3-manifolds, Amer. J. Math. 84 (1962), 1-7. MR 142125
  • [N] J. Nielsen, Abbildungsklassen endlicher Ordnung, Acta Math. 75 (1942), 23-115. MR 13306
  • [S1] P. Scott, A new proof of the annulus and torus theorems, Amer. J. Math. 2 (1978), 241-277. MR 564473
  • [S2] P. Scott, There are no fake Seifert fibred spaces with infinite $\pi \sb{1}$, Ann. of Math. (2) 117 (1983), 35-70. MR 683801
  • [Th] W. P. Thurston, Three dimensional manifolds, Kleinian groups, and hyperbolic geometry, Proc. Sympos. Pure Math. 39 (1983), 87-111. MR 648524
  • [T] P. Tukia, Homeomorphic conjugates of Fuchsian groups, J. Reine. Agnew. Math. 391 (1988), 1-54. MR 961162
  • [W] S. Wolpert, Geodesic length functions and the Nielson problem, J. Differential Geom. 25 (1987), 275-296. MR 880186
  • [W1] F. Waldhausen, Gruppen mit zentrum und 3-dimensionale mannigfaltigkeiten, Topology 6 (1967), 505-517. MR 236930
  • [W2] F. Waldhausen, On the determination of some bounded 3-manifolds by their fundamental groups alone, Proc. Internat. Sympos. Topology, Hercy-Novi, Yugoslavia, 1968, pp. 331-332.
  • [W3] F. Waldhausen, On irreducible 3-manifolds which are sufficiently large, Ann. of Math. (2) 87 (1968), 56-88. MR 224099
  • [Z] H. Zieschang, Finite groups of mapping classes of surfaces, Lecture Notes in Math., vol. 875, Springer-Verlag, Berlin and New York, 1981. MR 643627

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DOI: https://doi.org/10.1090/S0273-0979-1991-16082-9

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