Linking topological spheres

Abstract

There is a topological embedding $\iota :{\mathbb{S}}^1\to {\mathbb{R}}^5$ such that ${\pi }_3({\mathbb{R}}^5\setminus \iota ({\mathbb{S}}^1))=0$. Therefore, no $3$-sphere can be linked with $\iota ({\mathbb{S}}^1)$.