An elementary exposition to topological overlap in the plane
Geometric Topology
2015-08-05 v1
Abstract
The aim of this text is to provide an elementary and self-contained exposition of Gromov's argument on topological overlap (the presentation is based on Gromov's work, as well as two follow-up papers of Matousek and Wagner, and of Dotterrer, Kaufman and Wagner). We also discuss a simple generalization in which the vertices are weighted according to some probability distribution. This allows to use von Neumann's minimax theorem to deduce a dual statement.
Cite
@article{arxiv.1508.00777,
title = {An elementary exposition to topological overlap in the plane},
author = {Amir Yehudayoff},
journal= {arXiv preprint arXiv:1508.00777},
year = {2015}
}
Comments
10 pages, 8 figures