Colored Tverberg problem, extensions and new results

2020/02/21 by Jojić, Duško, Panina, Gaiane, Živaljević, Rade T.
#05E45 #52A20 #52A35 #52C99 #55U10 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2002.09186

Abstract

We prove a "multiple colored Tverberg theorem" and a "balanced colored Tverberg theorem", by applying different methods, tools and ideas. The proof of the first theorem uses multiple chessboard complexes (as configuration spaces) and Eilenberg-Krasnoselskii theory of degrees of equivariant maps for non-free actions. The proof of the second result relies on high connectivity of the configuration space, established by discrete Morse theory.

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