Existential questions in (relatively) hyperbolic groups {\it and} Finding relative hyperbolic structures

Abstract

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". 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", we provide a general algorithm that recognizes the class of groups that are hyperbolic relative to abelian subgroups.

Two independant parts 23p + 9p, revised. To appear separately in Israel J. Math, and Bull. London Math. Soc. respectively

References in corpus (4)

• Combination of convergence groups
• Hadamard spaces with isolated flats
• The Isomorphism Problem for Toral Relatively Hyperbolic Groups
• Accidental parabolics and relatively hyperbolic groups

Cited by in corpus (8)

• Finite generating sets of relatively hyperbolic groups and applications to geodesic languages
• Stallings graphs for quasi-convex subgroups
• Decidability of the Elementary Theory of a Torsion-Free Hyperbolic Group
• Conjugacy classes of solutions to equations and inequations over hyperbolic groups
• Recognizing a relatively hyperbolic group by its Dehn fillings
• On suspensions, and conjugacy of hyperbolic automorphisms (and of a few more)
• Quantifier elimination algorithm to boolean combination of $\exists \forall$-formulas in the theory of a free group
• Groups acting freely on $\Lambda$-trees