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 $k,l\ge 2$ 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 $K\ast L$ embeds into ${\mathbb{R}}^{2(k+l+1)}$.

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