Approximating embeddings of polyhedra in codimension three

Bryant, J. L.

doi:10.1090/S0002-9947-1972-0307245-7

Approximating embeddings of polyhedra in codimension three
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Trans. Amer. Math. Soc. 170 (1972), 85-95 Request permission

Abstract:

Let $P$ be a $p$-dimensional polyhedron and let $Q$ be a PL $q$-manifold without boundary. (Neither is necessarily compact.) The purpose of this paper is to prove that, if $q - p \geqslant 3$, then any topological embedding of $P$ into $Q$ can be pointwise approximated by PL embeddings. The proof of this theorem uses the analogous result for embeddings of one PL manifold into another obtained by Černavskiĭ and Miller.

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Seminar on combinatorial topology