Optimal bounds for the colored Tverberg problem

Günter Ziegler
Technische Universität Berlin

The "colored Tverberg problem" asks for a smallest size of the color classes in a (d+1)-colored point set C that forces the existence of an intersecting family of r "rainbow"
simplices with disjoint, multicolored vertex sets from C.

Using relative equivariant obstruction theory applied to a modified problem, we prove the optimal lower bound conjectured by Barany and Larman (1992) for the case of partition into r parts, if r+1 is a prime.

(Joint work with Pavle V. Blagojevic)

Presentation (PDF File)

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