Hyperbolic hydra.

DOI10.4171/GGD/212zbMath1318.20041arXiv1105.1535OpenAlexW3037232051MaRDI QIDQ2637230

Noel Brady, Will Dison, Timothy R. Riley

Publication date: 7 February 2014

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.1535

zbMATH Keywords

presentationshyperbolic groupsAckermann functionsfree subgroups of finite ranksubgroup distortionHydra groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Hyperbolic groups and nonpositively curved groups (20F67)

Related Items (3)

List of problems on discrete subgroups of Lie groups and their computational aspects ⋮ Algorithmically complex residually finite groups ⋮ Non-quasiconvex subgroups of hyperbolic groups via Stallings-like techniques

Cites Work

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• Hydra groups.
• Hyperbolic groups which fiber in infinitely many ways.
• Cannon-Thurston maps for trees of hyperbolic metric spaces
• Super-exponential distortion of subgroups of \(\text{CAT}(-1)\) groups.
• Distortion of surface groups in CAT(0) free-by-cyclic groups.
• On the Asphericity of Ribbon Disc Complements
• The Extrinsic Geometry of Subgroups and the Generalized Word Problem
• On the Existence of Flat Planes in Spaces of Non-Positive Curvature
• Solvable groups with polynomial Dehn functions

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