2020/01/17 by Salman Parsa, Parsa, Salman · 1 citation
Computer Science · Medicine · Mathematics · #Topological and Geometric Data Analysis #Advanced Neuroimaging Techniques and Applications #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2001.06506
We relate the embeddability of the simplicial complex [3]*K into ℝn+2 to that of K into ℝn. In brief, the embeddability of K into ℝn, in the metastable range 2n≥ 3(d+1), is equivalent to the embeddability of [3]*K into ℝn+2. We show moreover than the van Kampen obstruction of K vanishes if and only if the van Kampen obstruction of [3]*K vanishes. It follows that for d=2, embeddabilty of [3]*K is equivalent with the vanishing of the van Kampen obstruction for K, but not with the embeddability of K.