# Canonical representatives and equations in hyperbolic groups

@article{Rips1995CanonicalRA,
title={Canonical representatives and equations in hyperbolic groups},
author={Eliyahu Rips and Zlil Sela},
journal={Inventiones mathematicae},
year={1995},
volume={120},
pages={489-512}
}
• Published 1 December 1995
• Mathematics
• Inventiones mathematicae
SummaryWe use canonical representatives in hyperbolic groups to reduce the theory of equations in (torsion-free) hyperbolic groups to the theory in free groups. As a result we get an effective procedure to decide if a system of equations in such groups has a solution. For free groups, this question was solved by Makanin [Ma]|and Razborov [Ra]. The case of quadratic equations in hyperbolic groups has already been solved by Lysenok [Ly]. Our whole construction plays an essential role in the…
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