Optimal bounds for the colored Tverberg problem

  • Pavle V.M. Blagojević

    Freie Universität Berlin, Germany
  • Benjamin Matschke

    Bonn, Germany
  • Günter M. Ziegler

    Freie Universität Berlin, Germany


We prove a “Tverberg type” multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Bárány et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of B´ar´any & Larman (1992) that is tight in the prime case and asymptotically optimal in the general case. The proof is based on relative equivariant obstruction theory.

Cite this article

Pavle V.M. Blagojević, Benjamin Matschke, Günter M. Ziegler, Optimal bounds for the colored Tverberg problem. J. Eur. Math. Soc. 17 (2015), no. 4, pp. 739–754

DOI 10.4171/JEMS/516