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
  • Günter M. Ziegler

    Freie Universität Berlin, Germany
Barycenters of polytope skeleta and counterexamples to the Topological Tverberg Conjecture, via constraints cover
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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 “rr-fold Whitney trick” of Mabillard and Wagner (2014/2015) implies that the Topological Tverberg Conjecture for rr-fold intersections fails dramatically for all rr 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