Eliminating Higher-Multiplicity Intersections, I. A Whitney Trick for Tverberg-Type Problems

@article{Mabillard2015EliminatingHI,
title={Eliminating Higher-Multiplicity Intersections, I. A Whitney Trick for Tverberg-Type Problems},
author={Isaac Mabillard and Uli Wagner},
journal={CoRR},
year={2015},
volume={abs/1508.02349}
}

Motivated by topological Tverberg-type problems in topological combinatorics and by classical results about embeddings (maps without double points), we study the question whether a finite simplicial complex K can be mapped into R without triple, quadruple, or, more generally, r-fold points (image points with at least r distinct preimages), for a given multiplicity r ≥ 2. In particular, we are interested in maps f : K → R that have no r-Tverberg points, i.e., no r-fold points with preimages in r… CONTINUE READING