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 ⩽ 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.