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The Zeeman conjecture for unthickenable special polyhedra is equivalent to the Andrews-Curtis conjecture. (Russian) Zbl 0638.57002
A finite 2-dimensional CW-complex is called a special polyhedron, if the link of each vertex is homeomophic to the circle with 3 radii and the link of each other point of its 1-skeleton is homeomophic to the circle with 2 radii. In particular, the special polyhedron must have at least one vertex. The main result of the paper is the following theorem.
Theorem. The special polyhedron Q cannot be embedded in a 3-manifold. If Q 3-deforms to a 2-dimensional polyhedron X, then \(Q\times I\) collapses to a subset which is homeomorphic with X.
This implies that the Zeeman conjecture is true for each special polyhedron Q, which 3-deforms to the point and is unthickenable (i.e. cannot be embedded in a 3-manifold). The equivalence mentioned in the title is the consequence of this fact.
Reviewer: S.V.Matveev

57M20 Two-dimensional complexes (manifolds) (MSC2010)
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