Tesselations of<i>S</i>²and equations over torsion-free groups

Abstract

Let G be a torsion free group, F the free group generated by t . The equation r ( t ) = 1 is said to have a solution over G if there is a solution in some group that contains G . In this paper we generalize a result due to Klyachko who established the solution when the exponent sum of t is one.