FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2003, VOLUME 9, NUMBER 1, PAGES 259-262

Groups of signature (0;n;0)

P. Tumarkin

Abstract

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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 Si, 1 £ i £ n - 1, and denote by G the group generated by these mappings. Each Si 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 G.

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