75 research outputs found
Residual properties of 3-manifold groups I: Fibered and hyperbolic 3-manifolds
Let be a prime. In this paper, we classify the geometric 3-manifolds
whose fundamental groups are virtually residually . Let be a
virtually fibered 3-manifold. It is well-known that is residually
solvable and even residually finite solvable. We prove that is always
virtually residually . Using recent work of Wise, we prove that every
hyperbolic 3-manifold is either closed or virtually fibered and hence has a
virtually residually fundamental group. We give some generalizations to
pro- completions of groups, mapping class groups, residually torsion-free
nilpotent 3-manifold groups and central extensions of residually groups.Comment: 25 pages. Complete rewrit
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