Skip to main content

Groups of Signature (0; n; 0)

Abstract

Let M be an ideal polygon with 2n − 2 vertices. Consider a pairing of the symmetrical (with respect to some fixed diagonal) sides of M by mappings S i , 1 ⩽ in − 1, and denote by Γ the group generated by these mappings. Each S i depends on one parameter. We prove a necessary and sufficient condition for the possibility of choosing these parameters so that our polygon M would be a fundamental domain for the action of Γ.

This is a preview of subscription content, access via your institution.

REFERENCES

  1. 1.

    H. Poincare, Oeuvres, Vol. II, Gauthier-Villars, Paris (1916).

    Google Scholar 

  2. 2.

    A. Beardon, The Geometry of Discrete Groups, Springer (1983).

Download references

Author information

Affiliations

Authors

Additional information

__________

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 1, pp. 259–262, 2003.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Tumarkin, P. Groups of Signature (0; n; 0). J Math Sci 128, 3501–3503 (2005). https://doi.org/10.1007/s10958-005-0285-x

Download citation

Keywords

  • Fundamental Domain
  • Ideal Polygon