Corpus ID: 201645330

# Stronger counterexamples to the topological Tverberg conjecture

@article{Avvakumov2019StrongerCT,
title={Stronger counterexamples to the topological Tverberg conjecture},
author={S. Avvakumov and R. Karasev and A. Skopenkov},
journal={ArXiv},
year={2019},
volume={abs/1908.08731}
}
• Published 2019
• Mathematics, Computer Science
• ArXiv
• Denote by $\Delta_N$ the $N$-dimensional simplex. A map $f\colon \Delta_N\to\mathbb R^d$ is an almost $r$-embedding if $f\sigma_1\cap\ldots\cap f\sigma_r=\emptyset$ whenever $\sigma_1,\ldots,\sigma_r$ are pairwise disjoint faces. A counterexample to the topological Tverberg conjecture asserts that if $r$ is not a prime power and $d\ge2r+1$, then there is an almost $r$-embedding $\Delta_{(d+1)(r-1)}\to\mathbb R^d$. We improve this by showing that if $r$ is not a prime power and \$N:=(d+1)r-r\Big… CONTINUE READING