Finding relative hyperbolic structures
نویسنده
چکیده
This arXived paper has two independant parts, that are improved and corrected versions of different parts of a single paper, once named “On equations in relatively hyperbolic groups”. The first part is entitled “Existential questions in (relatively) hyperbolic groups” (to appear in Israel J. Math.). We study there the existential theory of torsion free hyperbolic and relatively hyperbolic groups, in particular those with virtually abelian parabolic subgroups. We show that the satisfiability of systems of equations and inequations is decidable in these groups. In the second part, called “Finding relative hyperbolic structures” (to appear in Bull. London Math. Soc.), we provide a general algorithm that recognizes the class of groups that are hyperbolic relative to abelian subgroups.
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