  We show that there exist non-trivial piecewise-linear (PL) knots with
isolated singularities $S^{n-2}\subset S^n$, $n\geq 5$, whose complements have
the homotopy type of a circle. This is in contrast to the case of smooth, PL
locally-flat, and topological locally-flat knots, for which it is known that if
the complement has the homotopy type of a circle, then the knot is trivial.
