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 “-fold Whitney trick” of Mabillard and Wagner (2014/2015) implies that the Topological Tverberg Conjecture for -fold intersections fails dramatically for all that are not prime powers.
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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. 2107–2116DOI 10.4171/JEMS/881