Higher dimensional links in a simplicial complex embedded in a sphere

We show that any embedding of the n-skeleton of a (2n+ 3)-dimensional simplex into the (2n + 1)-dimensional sphere contains a nonsplittable link of two n-dimensional spheres. 1. Introduction. Throughout this paper we work in the piecewise linear category. Conway and Gordon showed in [1] that any embedding of the complete graph over six vertices into the 3-space contains a pair of nontrivially linked circles. We refer the reader to [6], [2], [4], [3] etc. for related works. In this paper w