A manifold that does not contain a compact core (Q1295184)

It is known that a core of a (noncompact) manifold is a submanifold with the property that the inclusion of the submanifold into the manifold is a homotopy equivalence. In the paper under review the author proves by example that a manifold may fail to contain a compact core even though the manifold has the homotopy type of a finite complex.