Arithmeticity, Discreteness and Volume

@inproceedings{Gehring1997ArithmeticityDA,
  title={Arithmeticity, Discreteness and Volume},
  author={Frederick W. Gehring},
  year={1997}
}
We give an arithmetic criterion which is sufficient to imply the discreteness of various two-generator subgroups of PSL(2, c). We then examine certain two-generator groups which arise as extremals in various geometric problems in the theory of Kleinian groups, in particular those encountered in efforts to determine the smallest co-volume, the Margulis constant and the minimal distance between elliptic axes. We establish the discreteness and arithmeticity of a number of these extremal groups… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 43 references

Commensurability classes and volumes of hyperbolic 3-manifolds, Ann

  • A. Borel
  • Scuola Norm. Sup. Pisa
  • 1981
Highly Influential
16 Excerpts

Commutators, collars and the geometry of Möbius groups

  • F. W. Gehring, G. J. Martin
  • J. d’Analyse Math
  • 1994
Highly Influential
8 Excerpts

Arithmétique des algèbres de quaternions

  • M-F. Vignéras
  • Lecture Notes in Math., vol. 800, Springer–Verlag
  • 1980
Highly Influential
5 Excerpts

The volume of hyperbolic 3–folds with p–torsion, p ≥ 6. Centre for Mathematics and its Applications

  • F. W. Gehring, G. J. Martin
  • 1995
Highly Influential
4 Excerpts

Commensurability classes of arithmetic Kleinian groups and their Fuchsian subgroups, Math

  • C. Maclachlan, A. W. Reid
  • Proc. Camb. Phil. Soc
  • 1987
Highly Influential
4 Excerpts

The geometry of discrete groups, Springer–Verlag

  • A. F. Beardon
  • MR
  • 1983
Highly Influential
6 Excerpts

Groups of integral representation type, Pacific

  • H. Bass
  • J. Math
  • 1980
Highly Influential
6 Excerpts

A characterization of arithmetic Fuchsian groups

  • K. Takeuchi
  • J. Math. Soc. Japan
  • 1975
Highly Influential
5 Excerpts

Similar Papers

Loading similar papers…