Abstract
Let [Formula: see text] and [Formula: see text] be the complementary regions of a closed hypersurface [Formula: see text] in [Formula: see text]. We use the Massey product structure in [Formula: see text] to limit the possibilities for [Formula: see text] and [Formula: see text]. We show also that if [Formula: see text] then it may be modified by a 2-knot satellite construction, while if [Formula: see text] and [Formula: see text] is abelian then [Formula: see text] or [Formula: see text]. Finally we use TOP surgery to propose a characterization of the simplest embeddings of [Formula: see text].
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