## Retracting compact 3-manifolds onto their boundary components.(English)Zbl 0998.57042

Summary: Let $$X$$ be a compact 3-manifold and $$A$$ a boundary component of $$X$$ to which $$X$$ retracts. We propose the problem of classifying such $$(X,A)$$ up to PL homeomorphisms in a suitable class of manifolds. We give a complete solution in a special case. We show in this case there are exactly twenty-four basic pairs $$(X,A)$$ and all other cases are obtained from these by some obvious modifications. If $$A$$ is assumed to be different from a 2-sphere, there are six basic pairs.

### MSC:

 57N10 Topology of general $$3$$-manifolds (MSC2010) 54C15 Retraction 57M99 General low-dimensional topology 57Q99 PL-topology

retraction
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### References:

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