van Kampen-Flores theorem for cell complexes

DOI10.1007/S00454-023-00559-0arXiv2109.09919OpenAlexW4386541324MaRDI QIDQ6204772

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Publication date: 2 April 2024

Published in: (Search for Journal in Brave)

Abstract: The van Kampen-Flores theorem states that the $n$-skeleton of a $(2n+2)$-simplex does not embed into $mathbb{R}^{2n}$. We give two proofs for its generalization to a continuous map from a skeleton of a certain regular CW complex 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 $mathbb{R}^{2n+1}$.

Full work available at URL: https://arxiv.org/abs/2109.09919

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