Generators and Relations for Discontinuous Groups

  • Bruno Zimmermann
Part of the NATO ASI Series book series (ASIC, volume 333)


This paper contains the Bass-Serre theory generalizing free products with amalgamation and HNNextensions; the structure of finite extensions of free groups and applications to finite group actions on surfaces; and the theory of planar discontinuous groups.


Finite Group Fundamental Group Cayley Graph Free Product Finite Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bea.
    Beardon, A.L., The Geometry of Discrete Groups. Graduate Texts in Mathematics 91. Springer 1983.Google Scholar
  2. Bes.
    Best, L.A., On torsion-free discrete subgroups of PSL(2,C) with compact orbit space. Can. J. Math. 23, (1971) 451–460.MathSciNetzbMATHCrossRefGoogle Scholar
  3. BLW.
    Brunner, A., Lee, Y., Wielenberg, N., Polyhedral groups and graph amalgamation products. Topology Appl. 20, (1985) 289–304.MathSciNetzbMATHCrossRefGoogle Scholar
  4. H1.
    Hempel, J., 3-manifolds. Annals of Math. Studies 86. Princeton University Press 1976.Google Scholar
  5. H2.
    Hempel, J., Orientation-reversing involutions and the first Betti number of finite coverings of 3-manifolds. Invent. Math. 67, (1982) 133–142.MathSciNetzbMATHCrossRefGoogle Scholar
  6. KPS.
    Karras, A., Pietrowsky, A., Solitar, D., Finite and infinite extensions of free groups. J. Austr. Math. Soc. 16, (1972) 458–466.CrossRefGoogle Scholar
  7. L.
    Lehner, J., Discontinuous Groups and Automorphic Functions. Math. Surveys Amer. Math. Soc. 1964.Google Scholar
  8. Ma.
    Maskit, B., On Poincaré’s theorem for fundamental polygons. Adv. in Math. 7, (1971) 219–230.MathSciNetzbMATHCrossRefGoogle Scholar
  9. Mi.
    Miller, A., A group theoretic characterization of the 2-dimensional spherical groups. Canad. Math. Bull. 32, (1989) 459–466.MathSciNetzbMATHCrossRefGoogle Scholar
  10. MMZ1.
    Miller, A., McCullough, D., Zimmermann, B., Group actions on handle bodies. Proc. London Math. Soc. 59, (1989) 373–416.MathSciNetzbMATHCrossRefGoogle Scholar
  11. MMZ2.
    Miller, A., McCullough, D., Zimmermann, B., Group actions on bounded surfaces. To appear in J. Pure Appl. Math. 1990.Google Scholar
  12. MZ.
    Miller, A., Zimmermann, B., Large groups of symmetries of handle bodies. Proc. Amer. Math. Soc. 106, (1989) 829–838.MathSciNetzbMATHCrossRefGoogle Scholar
  13. S.
    Serre, J.P., Trees. Springer 1980.Google Scholar
  14. SW.
    Scott, P., Wall, T., Topological methods in group theory. Homological Group Theory. London Math. Soc. Lecture Notes 36, Cambridge University Press 1979.Google Scholar
  15. Z1.
    Zimmermann, B., Über Homöomorphismen n-dimensionaler Henkelkörper und endliche Erweiterungen von Schottky-Gruppen. Comment. Math. Helv. 56, (1981) 474–486.MathSciNetzbMATHCrossRefGoogle Scholar
  16. Z2.
    Zimmermann, B., Das Nielsensche Realisierungsproblem für hinreichend grosse 3-Mannigfaltigkeiten. Math. Z. 180, (1982) 349–359.MathSciNetzbMATHCrossRefGoogle Scholar
  17. Z3.
    Zimmermann, B., Über Abbildungsklassen von Henkelkörpern. Arch. Math. 33, (1979) 379–382.CrossRefGoogle Scholar
  18. Zie.
    Zieschang, H., Finite groups of mapping classes of surfaces. Lecture Notes in Mathematics 875 Springer 1981.Google Scholar
  19. ZVC.
    Zieschang, H., Vogt, E., Coldewey, H.D., Surfaces and planar discontinuous groups. Lecture Notes in Mathematics 835. Springer 1980.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • Bruno Zimmermann
    • 1
  1. 1.Dipartimento di Scienze MatematicheUniversità degli Studi di TriesteTriesteItaly

Personalised recommendations