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.


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


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