SPECIAL SPINES OF PIECEWISE LINEAR MANIFOLDS
Sergey V. Matveev · Mathematics of the USSR-Sbornik · 1973
A class of so-called special polyhedra is defined for each . The following theorems are proved:1. Every piecewise linear manifold with boundary can be collapsed to some -dimensional special polyhedron.2. The manifold is uniquely determined by this special polyhedron.3. If , then any special polyhedron can be thickened to an -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 , where is a contractible polyhedron.Figures: 4. Bibliography: 6 items.