2 problems

Conjectured failure of regular-neighborhood invariance. The property fails in each of the following cases: (e) $M=S^{2k}$ and $K=\Sigma(S^{k-1}\sqcup S^{k-1})$, where $f$ and $g$ c…

A thickening is a regular neighborhood of a PL submanifold. In codimension $q=1$, the known thickenings are $I$-bundles. Schoenflies conjecture. There are no codimension-one thicke…