, Volume 120, Issue 1, pp 489-512

Canonical representatives and equations in hyperbolic groups

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We 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 solution of the isomorphism problem for (torsion-free) hyperbolic groups ([Se1],[Se2]).

Oblatum 1-1992 & 1-XI-1994
Partially supported by NSF grant DMS-9305848