Special spines of piecewise linear manifolds

S. V. Matveev

Sbornik. Mathematics, Tome 21 (1973) no. 2, pp. 279-291

Résumé

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.