Embeddability of joins and products of polyhedra - Melikhov, Sergey A. (Topological Methods in Nonlinear Analysis, 2022)
We present a short proof of S. Parsa’s theorem that there exists a compact n-polyhedron P, n2, non-embeddable in ^2n, such that P*P embeds in ^4n+2. This proof can serve as a showcase for the use of geometric cohomology. We also show that a compact n-polyhedron X embeds in ^m, m3(n+1)/2, if either itemize X*K embeds in ^m+2k, where K is the (k-1)-skeleton of the 2k-simplex; or X*L embeds in ^m+2k, where L is the join of k copies of the 3-point set; or X is acyclic and X(triod)^k embeds in ^m+2k. itemize