English

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.

Keywords

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

R2 v1 2026-06-22T10:26:07.134Z