2002/07/01 by Siniša T. Vrećica, Sinisa T. Vrecica, Vrecica, Sinisa T.
Computer Science · Mathematics · #52A35 #55M20 #55R25 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Topological and Geometric Data Analysis #math.AT #math.CO #msc:52A35 #msc:55M20 #msc:55R25
paper · pdf · doi:10.48550/arxiv.math/0207011
arxiv created 2002/07/01 · openalex publication_date 2002/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1989 H. Tverberg proposed a quite general conjecture in Discrete geometry, which could be considered as the common basis for many results in Combinatorial geometry and at the same time as a discrete analogue of the common transversal theorems. It implies or contains as the special cases many classical "coincidence" results such as Radon's theorem, Rado's theorem, the Ham-sandwich theorem, the nonembeddability results (of graphs in the plane) etc. The main goal of this note is to verify this conjecture in one new, non-trivial case. We obtain the continuous version of the conjecture. So, it is not surprising that we use topological methods, or more precisely the methods of equivaiant topology and the characteristic classes.