On embeddability of joins and their `factors'

S. Parsa; A. Skopenkov

doi:10.1016/j.topol.2023.108409

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arXiv · 2003.12285

On embeddability of joins and their `factors'

S. Parsa·A. Skopenkov

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Abstract

We present a short and clear proof of the following particular case of a 2006 result of Melikhov-Schepin: Let $K$ be a $k$-dimensional simplicial complex and $K*[3]$ the union of three cones over $K$ along their common bases. If $2d\ge3k+3$ and $K*[3]$ embeds into $\mathbb R^{d+2}$, then $K$ embeds into $\mathbb R^d$. We also present a generalization of this theorem. The proofs are based on the Haefliger-Weber `configuration spaces' embeddability criterion, equivariant suspension theorem and simple properties of joins and cones.

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S. Parsa, A. Skopenkov. 2020-03-27. On embeddability of joins and their `factors'. https://doi.org/10.1016/j.topol.2023.108409

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