2020/05/11 by Florian Frick, Pablo Soberón, Frick, Florian +1 · 1 citation
Computer Science · Mathematics · #52A35 #55S35 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2005.05251
openalex publication_date 2020/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Tverberg-type theory aims to establish sufficient conditions for a simplicial complex Σ such that every continuous map f\colon Σ→ ℝd maps q points from pairwise disjoint faces to the same point in ℝd. Such results are plentiful for q a power of a prime. However, for q with at least two distinct prime divisors, results that guarantee the existence of q-fold points of coincidence are non-existent -- aside from immediate corollaries of the prime power case. Here we present a general method that yields such results beyond the case of prime powers. In particular, we prove previously conjectured upper bounds for the topological Tverberg problem for all q.