Abstract
THIS PAPER is a study of a special class of toroidal decompositions of 3-manifolds called Bing-Whitehead decompositions. It is well known that a Bing-Whitehead decomposition of a 3-manifold is shrinkable if all successive stages are Bing nested; but it is not shrinkable if all successive stages are Whitehead nested. (See Figs 1 and 2.) Consider a Bing-Whitehead decomposition of a 3-manifold which is defined by h, successive Bing nested stages. followed by 1 Whitehead nested stage, followed by h, successive Bing nested stages, followed by 1 Whitehead nested stage, . . The principal result of this paper is that this decomposition is shrinkable if and only if
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