To S. Parsa's theorem on embeddability of joins

Abstract

The purpose of this short note is to guide a reader to a reliable reference for the following result of S. Parsa: For any $k,l\ge2$ there exist simplicial complexes $K, L$ of dimensions $k,l$ such that $K$ does not embed into $\mathbb R^{2k}$, and $L$ does not embed into $\mathbb R^{2l}$, but the join $K*L$ embeds into $\mathbb R^{2(k+l+1)}$.