Canonical Representatives and Equations in Hyperbolic Groups

摘要

Canonical representatives in hyperbolic groups are used to reduce the theory ofequations in (torsion-free) hyperbolic groups to the theory in free groups. As a result the authors get an effective procedure to decide if a system of equations in such groups has a solution. For free groups, the question was solved by Makanin and Razborov. The case of quadratic equations in hyperbolic groups has already been achieved by Lysenok.