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

Abstract

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.

arXiv comment6 pages. This manuscript subsumes arxiv:1502.00947 and arxiv:1411.4417. J. Europ. Math. Soc. (JEMS), in press