## 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.

### MSC:

 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

### Keywords:

3-manifolds; fundamental groups; residually free groups
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### References:

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