Van Kampen-Flores theorem for cell complexes

Daisuke Kishimoto; Takahiro Matsushita

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arXiv · 2109.09919

Van Kampen-Flores theorem for cell complexes

Daisuke Kishimoto·Takahiro Matsushita

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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 (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 $\mathbb{R}^{2n+1}$.

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Daisuke Kishimoto, Takahiro Matsushita. 2021-09-21. Van Kampen-Flores theorem for cell complexes. https://arxiv.org/abs/2109.09919

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