Relative hyperbolization of (one-ended hyperbolic)-by-cyclic groups
Copyright policy )Relative hyperbolization of (one-ended hyperbolic)-by-cyclic groups
We show that the semi-direct product of a one-ended torsion-free word-hyperbolic group with $\integers$, given through an automorphism $\alpha{:}\, G \,{\to}\, G$, is a hyperbolic group relative to certain canonical subgroups of $G$ on which $\alpha$ acts periodically or with linear growth.
Fundamental group, presentations, free differential calculus, Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, torsion-free word-hyperbolic groups, Topological methods in group theory, automorphisms, mapping torus groups, semi-direct products, surface groups, surface homeomorphism, relative hyperbolicity, Hyperbolic groups and nonpositively curved groups, Automorphisms of infinite groups, mapping-torus, [MATH.MATH-MG] Mathematics [math]/Metric Geometry [math.MG], Geometric group theory, graphs of groups, combination theorem
Fundamental group, presentations, free differential calculus, Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, torsion-free word-hyperbolic groups, Topological methods in group theory, automorphisms, mapping torus groups, semi-direct products, surface groups, surface homeomorphism, relative hyperbolicity, Hyperbolic groups and nonpositively curved groups, Automorphisms of infinite groups, mapping-torus, [MATH.MATH-MG] Mathematics [math]/Metric Geometry [math.MG], Geometric group theory, graphs of groups, combination theorem
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