Residually free 3-manifolds. (English) Zbl 1194.57005

Summary: We classify those compact 3-manifolds with incompressible toral boundary whose fundamental groups are residually free. For example, if such a manifold \(M\) is prime and orientable and the fundamental group of \(M\) is nontrivial then \(M\cong\Sigma\times S^1\), where \(\Sigma\) is a surface.


57M05 Fundamental group, presentations, free differential calculus
20E26 Residual properties and generalizations; residually finite groups
57N10 Topology of general \(3\)-manifolds (MSC2010)
20E05 Free nonabelian groups
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