Barycenters of polytope skeleta and counterexamples to the Topological Tverberg Conjecture, via constraints

Pavle V.M. Blagojević; Florian Frick; Günter M. Ziegler

doi:10.4171/jems/881

JournalsjemsVol. 21, No. 7pp. 2107–2116

Barycenters of polytope skeleta and counterexamples to the Topological Tverberg Conjecture, via constraints

Pavle V.M. Blagojević
Institut SANU, Belgrad, Serbia and Freie Universität Berlin, Germany
Florian Frick
Carnegie Mellon University, Pittsburgh, USA
- MathSciNet
- zbMATH Open
Günter M. Ziegler
Freie Universität Berlin, Germany
- MathSciNet
- zbMATH Open

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Abstract

Using the authors’ 2014 “constraint method,” we give a short proof for a 2015 result of Dobbins on representations of a point in a polytope as the barycenter of points in a skeleton, and show that the “ $r$ -fold Whitney trick” of Mabillard and Wagner (2014/2015) implies that the Topological Tverberg Conjecture for $r$ -fold intersections fails dramatically for all $r$ that are not prime powers.

Cite this article

Pavle V.M. Blagojević, Florian Frick, Günter M. Ziegler, Barycenters of polytope skeleta and counterexamples to the Topological Tverberg Conjecture, via constraints. J. Eur. Math. Soc. 21 (2019), no. 7, pp. 2107–2116

DOI 10.4171/JEMS/881