Subgroup separability, knot groups and graph manifolds

DOI10.1090/S0002-9939-00-05574-XzbMath0967.20018MaRDI QIDQ4523190

Daniel T. Wise, Graham A. Niblo

Publication date: 8 January 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

subgroups of finite indexfree products with amalgamationsubgroup separable groups3-manifold groupsknot groups

Mathematics Subject Classification ID

Fundamental group, presentations, free differential calculus (57M05) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Residual properties and generalizations; residually finite groups (20E26) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34)

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Subgroup separability of certain generalized free products of nilpotent-by-finite groups. ⋮ Hydra group doubles are not residually finite. ⋮ Residual finiteness of infinite amalgamated products of cyclic groups. ⋮ Free by cyclic groups and linear groups with restricted unipotent elements ⋮ On subgroup separability of free‐by‐cyclic and deficiency 1 groups ⋮ Right-angled Artin groups and curve graphs of nonorientable surfaces ⋮ Limit groups over coherent right-angled Artin groups are cyclic subgroup separable ⋮ Profinite rigidity of graph manifolds and JSJ decompositions of 3-manifolds ⋮ The submonoid and rational subset membership problems for graph groups. ⋮ On the profinite topology of right-angled Artin groups. ⋮ Immersed and virtually embedded \(\pi_1\)-injective surfaces in graph manifolds ⋮ Quasi-potency and cyclic subgroup separability. ⋮ Symplectic $\mathbf{S}^{1} \times N^3$, subgroup separability, and vanishing Thurston norm ⋮ Double coset separability of abelian subgroups of hyperbolic $n$-orbifold groups ⋮ Profinite properties of graph manifolds ⋮ Subgroup separability of Artin groups ⋮ A characterization of virtually embedded subsurfaces in $3$-manifolds

Cites Work

• \(\pi_1\)-injective surfaces in graph manifolds
• Convergence groups and Seifert fibered 3-manifolds
• Subgroup separability and 3-manifold groups
• Subgroup separability of the figure 8 knot group.
• Correction to ‘Subgroups of Surface Groups are almost Geometric’
• A note on groups with separable finitely generated subgroups
• Three dimensional manifolds, Kleinian groups and hyperbolic geometry
• Knots
• Convergence groups are Fuchsian groups
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