Topological Tverberg Theorem: the proofs and the counterexamples
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 73 (2018) no. 2, pp. 355-362
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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
Mots-clés : $\mathscr{O}$-orientation.
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S. B. Shlosman. Topological Tverberg Theorem: the proofs and the counterexamples. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 73 (2018) no. 2, pp. 355-362. http://geodesic.mathdoc.fr/item/RM_2018_73_2_a3/

[1] I. Bárány, P. V. M. Blagojević, G. M. Ziegler, “Tverberg's theorem at 50: extensions and counterexamples”, Notices Amer. Math. Soc., 63:7 (2016), 732–739 | DOI | MR | Zbl

[2] I. Bárány, S. B. Shlosman, A. Szücs, “On a topological generalization of a theorem of Tverberg”, J. London Math. Soc. (2), 23:1 (1981), 158–164 | DOI | MR | Zbl

[3] P. V. M. Blagojević, F. Frick, G. M. Ziegler, Barycenters of polytope skeleta and counterexamples to the topological Tverberg conjecture, via constraints, 2015, 6 pp., arXiv: 1510.07984

[4] F. Frick, “Counterexamples to the topological Tverberg conjecture”, Oberwolfach Rep., 12 (2015), 318–322

[5] M. Gromov, “Singularities, expanders and topology of maps. Part 2: From combinatorics to topology via algebraic isoperimetry”, Geom. Funct. Anal., 20:2 (2010), 416–526 | DOI | MR | Zbl

[6] M. Ozaydin, Equivariant maps for the symmetric group, preprint, Univ. of Wisconsin-Madison, 1987, 17 pp. http://digital.library.wisc.edu/1793/63829

[7] A. B. Skopenkov, “Topologicheskaya gipoteza Tverberga”, UMN, 73:2(440) (2018)

[8] H. Tverberg, “A generalization of Radon's theorem”, J. London Math. Soc., 41 (1966), 123–128 | DOI | MR | Zbl

[9] A. Yu. Volovikov, “On a topological generalization of the Tverberg theorem”, Math. Notes, 59:3 (1996), 324–326 | DOI | DOI | MR | Zbl