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 $S$_i, $1$£ i £ n - 1, and denote by $$G the group generated by these mappings. Each $S$_i depends on one parameter. We prove a necessary and sufficient condition for the possibility of choosing these parameters so that our polygon $M$ would be a fundamental domain for the action of $$G.

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Last modified: April 4, 2004.