2021/01/26 by Hasui, Sho, Kishimoto, Daisuke, Takeda, Masahiro +1
#52A37 #55R80 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2101.10596
The topological Tverberg theorem states that any continuous map of a (d+1)(r-1)-simplex into the Euclidean d-space maps some points from r pairwise disjoint faces of the simplex to the same point whenever r is a prime power. We substantially generalize this theorem to continuous maps of certain CW complexes, including simplicial ((d+1)(r-1)-1)-spheres, into the Euclidean d-space. We also discuss the atomicity of the Tverberg property.