Van Kampen-Flores theorem for cell complexes
Algebraic Topology
2023-08-07 v2
Abstract
The van Kampen-Flores theorem states that the -skeleton of a -simplex does not embed into . 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 -skeleton of a -simplex into .
Cite
@article{arxiv.2109.09919,
title = {Van Kampen-Flores theorem for cell complexes},
author = {Daisuke Kishimoto and Takahiro Matsushita},
journal= {arXiv preprint arXiv:2109.09919},
year = {2023}
}
Comments
10 pages, some of the results (especially Theorem 1.4 and Corollary 1.5) were improved, final version, to appear in Discrete & Computational Geometry