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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The authors are grateful to the referees for useful comments.
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The authors were partly supported by JSPS KAKENHI Grant Numbers JP17K05248 and JP19K03473 (Kishimoto), and JP19K14536 (Matsushita).
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Kishimoto, D., Matsushita, T. van Kampen–Flores Theorem for Cell Complexes. Discrete Comput Geom 71, 1081–1091 (2024). https://doi.org/10.1007/s00454-023-00559-0
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DOI: https://doi.org/10.1007/s00454-023-00559-0