Optimal bounds for the colored Tverberg problem
Combinatorics
2022-03-25 v3 Algebraic Topology
Abstract
We prove a "Tverberg type" multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Barany et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of Barany & Larman (1992) that is tight in the prime case and asymptotically optimal in the general case. The proof is based on relative equivariant obstruction theory.
Cite
@article{arxiv.0910.4987,
title = {Optimal bounds for the colored Tverberg problem},
author = {Pavle V. M. Blagojević and Benjamin Matschke and Günter M. Ziegler},
journal= {arXiv preprint arXiv:0910.4987},
year = {2022}
}
Comments
17 pages, 3 figures; revised version (February 2013), to appear in J. European Math. Soc. (JEMS)