Discreteness is undecidable

DOI10.1142/S0218196716500193zbMath1346.03035OpenAlexW2288531606MaRDI QIDQ2814676

Michael Kapovich

Publication date: 22 June 2016

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218196716500193

zbMATH Keywords

discrete subgroupsdecidability

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Decidability of theories and sets of sentences (03B25) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

Related Items (7)

Computability Models: Algebraic, Topological and Geometric Algorithms ⋮ Geometric algorithms for discreteness and faithfulness ⋮ List of problems on discrete subgroups of Lie groups and their computational aspects ⋮ Verifying the Straight-and-spaced Condition ⋮ A discreteness algorithm for 4-punctured sphere groups ⋮ Discreteness is undecidable ⋮ On the discreteness of states accessible via right-angled paths in hyperbolic space

Uses Software

• MathOverflow

Cites Work

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• Projective structures with degenerate holonomy and the Bers density conjecture
• Discreteness is undecidable
• Applications of a Computer Implementation of Poincare's Theorem on Fundamental Polyhedra
• On sequences of finitely generated discrete groups
• Cusps in complex boundaries of one-dimensional Teichmüller space
• Two-generator discrete subgroups of 𝑃𝑆𝐿(2,𝑅)

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