Van Kampen-Flores theorem for cell complexes

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

10 pages, some of the results (especially Theorem 1.4 and Corollary 1.5) were improved, final version, to appear in Discrete & Computational Geometry

References in corpus (1)

• Tverberg's theorem for cell complexes