Special spines of piecewise linear manifolds

A class of so-called special polyhedra is defined for each $n>1$. The following theorems are proved:
1. Every piecewise linear manifold $M^{n+1}$ with boundary can be collapsed to some $n$-dimensional special polyhedron.
2. The manifold $M^{n+1}$ is uniquely determined by this special polyhedron.
3. If $n\geqslant3$, then any special polyhedron can be thickened to an $(n+1)$-dimensional manifold.
The author also gives applications of the results obtained to a series of questions connected with the Zeeman conjecture about the collapsibility of $P^2\times I$, where $P^2$ is a contractible polyhedron.
Figures: 4.
Bibliography: 6 titles.