Optimal bounds for the colored Tverberg problem

Optimal bounds for the colored Tverberg problem

We prove a “Tverberg type” multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Bárány et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverb...

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Veröffentlicht in:Journal of the European Mathematical Society : JEMS 2015-01, Vol.17 (4), p.739-754
Hauptverfasser: Blagojević, Pavle, Matschke, Benjamin, Ziegler, Günter
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Algebraic topology
Convex and discrete geometry
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creator Blagojević, Pavle
Matschke, Benjamin
Ziegler, Günter
description We prove a “Tverberg type” multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Bárány et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of B´ar´any & Larman (1992) that is tight in the prime case and asymptotically optimal in the general case. The proof is based on relative equivariant obstruction theory.
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Convex and discrete geometry
title Optimal bounds for the colored Tverberg problem
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