Barycenters of polytope skeleta and counterexamples to the Topological Tverberg Conjecture, via constraints
Pavle V. M. Blagojević, Florian Frick, Günter M. Ziegler · Journal of the European Mathematical Society · 2019
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.