Intrinsic linking of a simplicial $n$-complex embedded in ${\mathbb{R}}^{2n}$

Abstract

We demonstrate the existence of minimal simplicial $n$-complexes which inevitably contain a nonsplittable two-component link formed by an $(n-1)$-sphere and an $n$-sphere in any embedding into ${\mathbb{R}}^{2n}$. This provides a higher-dimensional generalization of graphs that are not non-separating planar.

9 pages, 4 figures