Tverberg's theorem for cell complexes

Abstract

AbstractThe topological Tverberg theorem states that any continuous map of a ‐simplex into the Euclidean ‐space maps some points from pairwise disjoint faces of the simplex to the same point whenever is a prime power. We substantially generalize this theorem to continuous maps of certain CW complexes, including simplicial ‐spheres, into the Euclidean ‐space. We also discuss the atomicity of the Tverberg property.