Journal of Mathematical Sciences

, Volume 128, Issue 6, pp 3501–3503 | Cite as

Groups of Signature (0; n; 0)

  • P. Tumarkin


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.


Fundamental Domain Ideal Polygon 
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  1. 1.
    H. Poincare, Oeuvres, Vol. II, Gauthier-Villars, Paris (1916).Google Scholar
  2. 2.
    A. Beardon, The Geometry of Discrete Groups, Springer (1983).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • P. Tumarkin
    • 1
  1. 1.Moscow State UniversityMoscowRussia

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