Convergence groups are Fuchsian groups
David Gabai
Source: Bull. Amer. Math. Soc. (N.S.) Volume 25, Number 2 (1991), 395-402.
Primary Subjects: 57S25
Secondary Subjects: 20H10, 57N05, 57N10
Full-text: Open access
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Permanent link to this document: http://projecteuclid.org/euclid.bams/1183657188
Mathematical Reviews number (MathSciNet):
MR1102752
Zentralblatt MATH identifier:
0733.57022
References
[E] D. B. A. Epstein, Periodic flows on 3-manifolds, Ann. of Math. (2) 95 (1972), 66-82.
Zentralblatt MATH:
0231.58009
Mathematical Reviews (MathSciNet):
MR288785
[F1] C. D. Feustel, On the Torus theorem and its applications, Trans. Amer. Math. Soc. 217 (1976), 1-43.
Zentralblatt MATH:
0321.55006
Mathematical Reviews (MathSciNet):
MR394666
[F2] C. D. Feustel, On the torus theorem for closed 3-manifolds, Trans. Amer. Math. Soc. 217 (1976), 45-57.
Zentralblatt MATH:
0321.55007
Mathematical Reviews (MathSciNet):
MR394667
[G] D. Gabai, Convergence groups are Fuchsian groups, preprint.
Zentralblatt MATH:
0785.57004
Mathematical Reviews (MathSciNet):
MR1189862
[GH] C. Gordon and W. Heil, Cyclic normal subgroups of fundamental groups of 3-manifolds, Topology 14 (1975), 305-309.
Zentralblatt MATH:
0331.57001
Mathematical Reviews (MathSciNet):
MR400232
[GM] F. W. Gehring and G. Martin, Discrete quasiconformal groups I, Proc. London Math. Soc. (3) 55 (1987), 331-358.
Zentralblatt MATH:
0628.30027
Mathematical Reviews (MathSciNet):
MR896224
[J] K. Johannson, Homotopy equivalences of 3-manifolds with boundary, Lecture Notes in Math., vol. 761, Springer-Verlag, Berlin and New York, 1979.
Zentralblatt MATH:
0412.57007
Mathematical Reviews (MathSciNet):
MR551744
[JS] W. H. Jaco and P. B. Shalen, Seifert fibered spaces in 3-manifolds, Mem. Amer. Math. Soc. 2 (1979).
Zentralblatt MATH:
0415.57005
Mathematical Reviews (MathSciNet):
MR539411
[K] S. P. Kerckhoff, The Nielsen realization problem, Ann. of Math. (2) 117 (1983), 235-265.
Zentralblatt MATH:
0528.57008
Mathematical Reviews (MathSciNet):
MR690845
[Kn] H. Kneser, Gerschlossene Flachen in dreidimensionalen Mannigfaltigkeiten, Jahres. der Deut. Math. Verein. 38 (1929), 248-260.
Jahrbuch database (Zbl):
55.0311.03
[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.
Zentralblatt MATH:
0108.36501
Mathematical Reviews (MathSciNet):
MR142125
[N] J. Nielsen, Abbildungsklassen endlicher Ordnung, Acta Math. 75 (1942), 23-115.
Zentralblatt MATH:
0027.26601
Mathematical Reviews (MathSciNet):
MR13306
[S1] P. Scott, A new proof of the annulus and torus theorems, Amer. J. Math. 2 (1978), 241-277.
Zentralblatt MATH:
0439.57004
Mathematical Reviews (MathSciNet):
MR564473
[S2] P. Scott, There are no fake Seifert fibred spaces with infinite $\pi \sb{1}$, Ann. of Math. (2) 117 (1983), 35-70.
Zentralblatt MATH:
0516.57006
Mathematical Reviews (MathSciNet):
MR683801
[Th] W. P. Thurston, Three dimensional manifolds, Kleinian groups, and hyperbolic geometry, Proc. Sympos. Pure Math. 39 (1983), 87-111.
Zentralblatt MATH:
0528.57009
Mathematical Reviews (MathSciNet):
MR648524
[T] P. Tukia, Homeomorphic conjugates of Fuchsian groups, J. Reine. Agnew. Math. 391 (1988), 1-54.
Zentralblatt MATH:
0644.30027
Mathematical Reviews (MathSciNet):
MR961162
[W] S. Wolpert, Geodesic length functions and the Nielson problem, J. Differential Geom. 25 (1987), 275-296.
Zentralblatt MATH:
0616.53039
Mathematical Reviews (MathSciNet):
MR880186
[W1] F. Waldhausen, Gruppen mit zentrum und 3-dimensionale mannigfaltigkeiten, Topology 6 (1967), 505-517.
Zentralblatt MATH:
0172.48704
Mathematical Reviews (MathSciNet):
MR236930
[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.
Zentralblatt MATH:
0202.54702
[W3] F. Waldhausen, On irreducible 3-manifolds which are sufficiently large, Ann. of Math. (2) 87 (1968), 56-88.
Zentralblatt MATH:
0157.30603
Mathematical Reviews (MathSciNet):
MR224099
[Z] H. Zieschang, Finite groups of mapping classes of surfaces, Lecture Notes in Math., vol. 875, Springer-Verlag, Berlin and New York, 1981.
Zentralblatt MATH:
0472.57006
Mathematical Reviews (MathSciNet):
MR643627
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