Year: 2026
Type: article
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.
DOI: 10.1090/proc/17409
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: CAREER: KKM-Type Theorems for Piercing Numbers, Mass Partition, and Fair Division, G1438018726, G1926179426, G1938303756, G2691427229, G3247244596, G3601956145, G5444156010, G5900057054, G6671297155, G7223544181, G7254398626, Postdoctoral Fellowship: MSPRF: Discrete Geometry and Geometric Transversal Theory
OpenAlex ID: W7124447355