Approximating codimension two embeddings of cells (Q1087189)

Given a topological embedding \(\alpha\) of a k-cell in a PL (i.e., piecewise linear) n-manifold, \textit{R. T. Miller} [Ann. Math., II. Ser. 95, 406-416 (1972; Zbl 0208.518)] devised an ingenious construction showing how to approximate \(\alpha\) by a PL embedding when \(k\leq n-3\). Exploding a widespread belief that Miller's argument is limited by the restriction \(k\leq n-3\), due to its dependence on engulfing-like methods, here the author very neatly retools it to obtain the \(k=n-2\) case. The fundamental new ingredient, to which the bulk of the paper is devoted, is a controlled piping lemma. Using somewhat different techniques the author earlier had produced PL approximations to topological embeddings of 2- cells in PL 4-manifolds [Michigan Math. J. 25, 19-27 (1978; Zbl 0365.57006)].