Abelian Subgroup Separability of Haken 3‐Manifolds and Closed Hyperbolic n‐Orbifolds

By E. Hamilton. 2001

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Mixed 3-manifolds are virtually special (2012, background): “ups of the pieces of Sin Mg i , which are virtually embedded in M g i by Theorem 2.1(3) or inﬁnite cyclic subgroups of the fundamental groups of the transitional tori, to which by [PW11, Cor 4.3] (or [Ham01]) we can also associate virtually embedded @–parallel annuli. All these stabilizers are separ”
Profinite properties of graph manifolds (2008, methodology): “1 (Hamilton, [8]) Let M be a compact 3-manifold with incompressible toral boundary.”
Distinguishing geometries using finite quotients (2014, background): “Conversely, if 1 1M contains no subgroups isomorphic to y Z(2) then, by Hamilton’s result that abelian subgroups of 3–manifold groups are separable [17], 1M contains no subgroups isomorphic to Z(2) and so, by the hyperbolization theorem, M is hyperbolic.”