Residual properties of 3-manifold groups I: Fibered and hyperbolic 3-manifolds

2009/10/11 by Koberda, Thomas
#20E26 (Primary) #57M10 #57N10 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.0910.2035

Abstract

Let p be a prime. In this paper, we classify the geometric 3-manifolds whose fundamental groups are virtually residually p. Let M=M³ be a virtually fibered 3-manifold. It is well-known that G=π₁(M) is residually solvable and even residually finite solvable. We prove that G is always virtually residually p. Using recent work of Wise, we prove that every hyperbolic 3-manifold is either closed or virtually fibered and hence has a virtually residually p fundamental group. We give some generalizations to pro-p completions of groups, mapping class groups, residually torsion-free nilpotent 3-manifold groups and central extensions of residually p groups.

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