Barycenters of Polytope Skeleta and Counterexamples to the Topological Tverberg Conjecture, via Constraints

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

Published 2015-10-27Version 1

Using the authors' 2014 "constraints 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.