Topological Tverberg Theorem: the proofs and the counterexamples

Senya Shlosman (1, 2)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - E5 Physique statistique et systèmes complexes

I describe the history of Topological Tverberg Theorem. I present some important constructions and discuss their properties. In particular, I describe in details the cell structure of the classifying space $K\left( S_{r},1\right),$ where $S_{r}$ is the permutation group. I also clarify some bibliographical issues.

Domaines: Combinatoire [math.CO]; Topologie géométrique [math.GT]

Senya Shlosman. Topological Tverberg Theorem: the proofs and the counterexamples. Russian Mathematical Surveys, 2018, 73 (2), pp.355. ⟨10.1070/RM9820⟩. ⟨hal-01779371⟩