zbMATH — the first resource for mathematics

Transformations of special spines and the Zeeman conjecture. (Russian) Zbl 0642.57003
A finite 2-dimensional CW-complex is called a special polyhedron, if the link of each vertex is homeomorphic to the circle with three radii and the link of each other point of its 1-skeleton is homeomorphic to the circle with two radii. A spine of a compact 3-manifold is special if it is a special polyhedron. Two kinds of elementary transformations of special polyhedra are introduced. The first transformation alters the polyhedron inside a small neighbourhood of a vertex, the second one inside a neighbourhood of an edge. Themain theorem affirms that any two special spines of each 3-manifold can be connected by a finite sequence of elementary transformations. This theorem enables one to reprove a result of D. Gillman and D. Rolfsen [Topology 22, 315-323 (1983; Zbl 0518.57007)] that the Zeeman conjecture is true for all special spines of the 3-ball.
Reviewer: S.V.Matveev

MSC:
 57M20 Two-dimensional complexes (manifolds) (MSC2010) 57N10 Topology of general $$3$$-manifolds (MSC2010)