The Bianchi groups are separable on geometrically finite subgroups

By Ian Agol, Darren D. Long, Alan W. Reid. 2001

107 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6cbb40caa0adfeb89453814a096c542c1b37d156

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Cohomological goodness and the profinite completion of Bianchi groups (2008, background): “So for example if one finds a hierarchy whose building blocks are geometrically finite, then one can use [1] directly in the proof.”
Tameness of hyperbolic 3-manifolds (2004, background): “Another application is that the fundamental group of the figure 8 knot complement is LERF (as well as for the fundamental groups of several other compact 3-manifold groups) [2, 30, 56, 41, 40].”
RESEARCH ANNOUNCEMENT: THE STRUCTURE OF GROUPS WITH A QUASICONVEX HIERARCHY (2009, unknown): “This generalizes the results of [1].”
Criteria for virtual fibering (2007, background): “3] (this was proven for cusped arithmetic 3-manifolds previously in [1]), and are thus virtually RFRS by Theorem 2.”
Finite index subgroups of graph products (2008, background): “We consider the n-cube CJ = [0, 1]J .”
Coxeter groups are virtually special (2010, background): “Our second application continues a line of work initiated by Scott in [22] (see also [1,9]) who proved that surface groups are subgroup separable, by showing that right-angled reflection groups of the hyperbolic plane have separable quasiconvex subgroups.”
All flat manifolds are cusps of hyperbolic orbifolds (2002, background): “The following is well-known and proved in [1] for example.”
Profinite properties of graph manifolds (2008, background): “The fundamental groups of all these 3-manifolds are known to be subgroup separable—that is, finitely generated subgroups are closed in the profinite topology [1].”
Hall’s Theorem for Limit Groups (2006, background): “Nevertheless, a connection with the Virtually Haken Conjecture has led to considerable interest in subgroup separability for the fundamental groups of hyperbolic 3-manifolds, where little is known (see, for example, [1], [14] and [28]).”