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 |
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Pages (from-to) | 255-264 |
Number of pages | 10 |
Journal | Discrete and Computational Geometry |
Volume | 58 |
Issue number | 2 |
DOIs | |
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