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A combination theorem for relatively hyperbolic groups. (English) Zbl 1074.57001
The authors adapt the combination theorem of Bestvina and Feighn to give sufficient conditions which ensure for a given graph of \(\delta\)-hyperbolic groups to be itself \(\delta\)-hyperbolic. As an application, for a given limit group, a \(\delta\)-hyperbolic space is constructed on which the group acts freely by isometries. The existence of such a space gives an answer to the question of whether limit groups are hyperbolic relative to their maximal non-cyclic abelian subgroups.

57M07 Topological methods in group theory
20F65 Geometric group theory
20F67 Hyperbolic groups and nonpositively curved groups
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