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}
}
  • E. Rips, Z. Sela
  • 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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