Special spines of piecewise linear manifolds
SV Matveev - Mathematics of the USSR-Sbornik, 1973 - iopscience.iop.org
Mathematics of the USSR-Sbornik, 1973•iopscience.iop.org
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 …
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 …
Abstract
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.
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