2021/09/21 by Daisuke Kishimoto, Kishimoto, Daisuke, Takahiro Matsushita +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2109.09919
openalex publication_date 2021/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The van Kampen-Flores theorem states that the n-skeleton of a (2n+2)-simplex does not embed into ℝ2n. We give two proofs for its generalization to a continuous map from a skeleton of a certain regular CW complex (e.g. a simplicial sphere) into a Euclidean space. We will also generalize Frick and Harrison's result on the chirality of embeddings of the n-skeleton of a (2n+2)-simplex into ℝ2n+1.