Intrinsic Linking of 2-complexes in $\mathbb{R}^4$

Abstract

We produce an infinite family of $2$-complexes that are intrinsically linked when embedded into four dimensions. In particular, we show that any embedding into $\mathbb{R}^4$ of the suspension of a graph containing $K_6$ as a minor contains a non-trivially linked 1 and 2-cycle.