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 ⩽ i ⩽ n − 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.
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H. Poincare, Oeuvres, Vol. II, Gauthier-Villars, Paris (1916).
A. Beardon, The Geometry of Discrete Groups, Springer (1983).
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 1, pp. 259–262, 2003.
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Tumarkin, P. Groups of Signature (0; n; 0). J Math Sci 128, 3501–3503 (2005). https://doi.org/10.1007/s10958-005-0285-x
- Fundamental Domain
- Ideal Polygon