An elementary exposition to topological overlap in the plane

2015/08/04 by Amir Yehudayoff, Yehudayoff, Amir
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1508.00777

10 pages, 8 figures

arxiv created 2015/08/04 · arxiv updated 2015/08/05

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.

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