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Uspekhi Mat. Nauk, 2018, Volume 73, Issue 2(440), Pages 175–182 (Mi umn9820)  

Topological Tverberg Theorem: the proofs and the counterexamples

S. B. Shlosmanabc

a Skolkovo Institute of Science and Technology
b Aix Marseille University, University of Toulon, CNRS, CPT, Marseille, France
c Institute for Information Transmission Problems of the Russian Academy of Sciences

Abstract: The history of the Topological Tverberg Theorem (TTT) is described. Some important constructions are presented, and their properties are discussed. In particular, there is a detailed description of the cell structure of the classifying space $K(S_r,1)$, where $S_r$ is the permutation group.
Bibliography: 9 titles.

Keywords: Tverberg Theorem, Borsuk–Ulam Theorem, $\mathscr{O}$-orientation.

Funding Agency Grant Number
Russian Science Foundation 14-50-00150
Agence Nationale de la Recherche ANR-11-LABX-0033
ANR-11-IDEX-0001-02
Part of this work was carried out in the framework of the Labex Archimede (grant ANR-11-LABX-0033) and of the A*MIDEX project (grant ANR-11-IDEX-0001-02), funded by the “Investissements d'Avenir” French Government programme managed by the French National Research Agency (ANR). Another part was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute) with the support of the Russian Science Foundation (grant no. 14-50-00150).


DOI: https://doi.org/10.4213/rm9820

Full text: PDF file (487 kB)
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English version:
Russian Mathematical Surveys, 2018, 73:2, 355–362

Bibliographic databases:

MSC: 52A35, 05B99, 01A65
Received: 06.03.2018

Citation: S. B. Shlosman, “Topological Tverberg Theorem: the proofs and the counterexamples”, Uspekhi Mat. Nauk, 73:2(440) (2018), 175–182; Russian Math. Surveys, 73:2 (2018), 355–362

Citation in format AMSBIB
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