2011/06/30 by Karasev, R. N. · 1 citation
#52A20 #55M20 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1106.6176
In this paper we study geometric coincidence problems in the spirit of the following problems by B. Grünbaum: How many affine diameters of a convex body in \mathbb Rn must have a common point? How many centers (in some sense) of hyperplane sections of a convex body in \mathbb Rn must coincide? One possible approach to such problems is to find topological reasons for multiple coincidences for a continuous map between manifolds of equal dimension. In other words, we need topological estimates for the multiplicity of a map. In this work examples of such estimates and their geometric consequences are presented.