An Elementary Exposition of Topological Overlap in the Plane

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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 Matoušek 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.

Original languageEnglish
Pages (from-to)255-264
Number of pages10
JournalDiscrete and Computational Geometry
Volume58
Issue number2
DOIs
StatePublished - 1 Sep 2017

Keywords

  • High dimensional expanders
  • Minimax theorem
  • Topological overlap property

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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