2017/05/10 by Pavle V. M. Blagojević, Blagojević, Pavle V. M., Albert Haase +3
Mathematics · #05E45 (Primary) #52A35 (Secondary) #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #math.AT #math.CO #math.MG #msc:05E45 #msc:52A35
paper · pdf · doi:10.48550/arxiv.1705.03624
16 pages, 4 figures
arxiv created 2017/05/10 · arxiv updated 2017/05/11
Bárány, Kalai, and Meshulam recently obtained a topological Tverberg-type theorem for matroids, which guarantees multiple coincidences for continuous maps from a matroid complex to d-dimensional Euclidean space, if the matroid has sufficiently many disjoint bases. They make a conjecture on the connectivity of k-fold deleted joins of a matroid with many disjoint bases, which would yield a much tighter result - but we provide a counterexample already for the case of k=2, where a tight Tverberg-type theorem would be a topological Radon theorem for matroids. Nevertheless, we prove the topological Radon theorem for the counterexample family of matroids by an index calculation, despite the failure of the connectivity-based approach.