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

TL;DR

This paper demonstrates the existence of certain $ ext{Z}$-compactifiable manifolds with noncompact boundary that are not pseudo-collarable, highlighting limitations in the relationship between these properties.

Contribution

It provides the first example of $ ext{Z}$-compactifiable manifolds with noncompact boundary that are not pseudo-collarable, challenging previous assumptions.

Findings

Existence of $ ext{Z}$-compactifiable manifolds with noncompact boundary that are not pseudo-collarable.

Clarification of the relationship between $ ext{Z}$-compactifiability and pseudo-collarability.

New insights into the structure of manifolds with boundary.

Abstract

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