Residual finiteness, QCERF, and fillings of hyperbolic groups

By Ian Agol, D. Groves, J. Manning. 2008

57 citations recorded by the source corpus.

We prove that if every hyperbolic group is residually finite, then every quasi-convex subgroup of every hyperbolic group is separable. The main tool is relatively hyperbolic Dehn filling.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cf35f0be04d7386fd26d2b2c57dcf9f6c39f0b9a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. J. Manning
2. Christopher Hruska
3. Martin R. Bridson
4. D. Groves
5. G. Hruska
6. Mark F. Hagen

In Geometry and Topology

1. D. Groves
2. Ian Agol
3. J. Manning
4. G. Hruska
5. Christopher Hruska
6. Alan W. Reid
7. Martin R. Bridson
8. Marston D. E. Conder

In Mathematical Physics

1. D. Groves
2. J. Manning
3. Ian Agol
4. G. Hruska
5. Christopher Hruska
6. Alan W. Reid
7. Martin R. Bridson
8. Marston D. E. Conder

Citations in the corpus

• Determining Fuchsian groups by their finite quotients (2014, background): “Recall that a smooth manifold X with a Riemannian metric g, symplectic form ω, and complex structure J is said to be Kähler if g(J(u), J(v)) = g(u, v) and g(Jp(u), v) = ω(u, v) for all p ∈ X and all tangent vectors u, v ∈ Tp(X).”
• Relative hyperbolicity and relative quasiconvexity for countable groups (2008, background): “As explained in the previous section, the most significant changes occur in our proof of (RH–6)) (RH–3), where we need to modify the Groves–Manning construction of combinatorial horoballs to account for non–finitely generated groups.”
• The virtual Haken conjecture (2012, background): “This does not change the coarse geometry of G or any of the statements we apply from [17, 1, 31, 23].”