$\mathcal{Z}$-compactifiable manifolds which are not pseudo-collarable

Abstract

It is shown that there exist $\mathcal{Z}$-compactifiable manifolds with noncompact boundary which fail to be pseudo-collarable.

21 pages, 5 figures. 2 more figures added. The original Prop. 4.4 has been removed due to an error. A new Prop. 4.5 is formed to replace the original Prop. 4.6 by assuming an extra hypothesis. The exposition is improved and expanded. To appear in Algebra. Geom. Topology. arXiv admin note: text overlap with arXiv:1807.11405

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