Approximating codimension two embeddings of cells
type: Item
instance of: scholarly article
title: Approximating codimension two embeddings of cells
zbMATH Open document ID: 0611.57011
author: G. A. Venema
published in: Pacific Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 57N35
Mathematics Subject Classification ID: 57N45
Mathematics Subject Classification ID: 57Q55
zbMATH DE Number: 3988274
zbMATH Keywords: approximate by PL embedding
zbMATH Keywords: codimension 2
zbMATH Keywords: controlled collapse
zbMATH Keywords: topological embedding
zbMATH Keywords: controlled piping lemma
reviewed by: Robert J. Daverman
MaRDI profile type: Publication
full work available at URL: pjm.1987.126.165
OpenAlex ID: W2053068491
DOI: 10.2140/PJM.1987.126.165
description: scientific article; zbMATH DE number 3988274