A topological product Tverberg theorem
Abstract
We prove a generalization of the topological Tverberg theorem. One special instance of our general theorem is the following: Let Δ \Delta denote the 8-dimensional simplex viewed as an abstract simplicial complex, and suppose that its vertices are arranged in a 3 × 3 3\times 3 array. Then for any continuous map f : Δ → R 3 f:\Delta \to \mathbb {R}^3 it is possible to partition the rows or the columns of the vertex array into two parts, such that the disjoint faces σ \sigma and τ \tau induced by the two parts satisfy f ( σ ) ∩ f ( τ ) ≠ ∅ f(\sigma )\cap f(\tau ) \neq \emptyset . Our result also has consequences for geometric transversals and topological Helly theorems.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Geometric and Algebraic Topology
Topological and Geometric Data Analysis
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 3
- Pages
- 1251–1260
- Publication date
- 16 January 2026
- Language
- EN