A finite 2-dimensional CW-complex P is called a standard (or special) polyhedron if the link of any vertex of P is homeomorphic to a circle with three radii and the link of any other point of its l-skeleton is homeomorphic to a circle with one diameter. Three transformations of standard polyhedra are defined, called standard moves. Moves I and III change a small neighbourhood of a vertex, move II changes a small neighbourhood of an edge. Let P, Q be two standard polyhedra. The following two results are proved: 1) P can be 3-deformed (in the sense of J. H. C. Whitehead) to Q if and only if P can be obtained from Q by a finite sequence of moves I, II, III and its inverses; 2) If P is a spine of a 3-manifold then Q is a spine of the same manifold if and only if P and Q can be related by moves I, II and its inverses only.

Standard moves for standard polyhedra and spines

PIERGALLINI, Riccardo
1988-01-01

Abstract

A finite 2-dimensional CW-complex P is called a standard (or special) polyhedron if the link of any vertex of P is homeomorphic to a circle with three radii and the link of any other point of its l-skeleton is homeomorphic to a circle with one diameter. Three transformations of standard polyhedra are defined, called standard moves. Moves I and III change a small neighbourhood of a vertex, move II changes a small neighbourhood of an edge. Let P, Q be two standard polyhedra. The following two results are proved: 1) P can be 3-deformed (in the sense of J. H. C. Whitehead) to Q if and only if P can be obtained from Q by a finite sequence of moves I, II, III and its inverses; 2) If P is a spine of a 3-manifold then Q is a spine of the same manifold if and only if P and Q can be related by moves I, II and its inverses only.
1988
262
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11581/244540
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