An Elementary Exposition of Topological Overlap in the Plane

Amir Yehudayoff

doi:10.1007/s00454-017-9910-y

An Elementary Exposition of Topological Overlap in the Plane

Amir Yehudayoff

Mathematics

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	255-264
Number of pages	10
Journal	Discrete and Computational Geometry
Volume	58
Issue number	2
DOIs	https://doi.org/10.1007/s00454-017-9910-y
State	Published - 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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10.1007/s00454-017-9910-y

Cite this

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An Elementary Exposition of Topological Overlap in the Plane

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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