Approximating polyhedra in codimension one spheres embedded in<i>s</i>^<i>n</i>by tame polyhedra

Abstract

We investigate properties of an (n -1)-sphere topologically embedded in the w-sphere S n (n ^ 6) implying that each (n -3)-dimensional polyhedron in can be homeomorphically approximated by polyhedra in that are tame in S n . In case bounds an w-cell, we relate these properties and the existence of homeomorphic approximations to by locally flat spheres "mostly" outside this n-cell. This leads to a negative result eliminating a natural generalization to Bing's Side Approximation Theorem.