The Topological Tverberg Theorem and winding numbers

Optimal bounds for the colored Tverberg problem

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 Bárány & Larman (1992) that is tight in the prime case and asymptotically optimal ...

Tverberg's theorem with constraints

We extend the topological Tverberg theorem in the following way: Pairs of points are forced to end up in different partition blocks. This leads to the concept of constraint graphs. In Tverberg’s theorem with constraints, we come up with a list of constraints graphs for the topological Tverberg theorem. The proof is based on connectivity results of chessboard-type complexes. Tverberg’s theorem w...

Tverberg graphs

The topological Tverberg theorem states that for any prime power q and continuous map from a (d + 1)(q − 1)-simplex to R, there are q disjoint faces Fi of the simplex whose images intersect. It is possible to put conditions on which pairs of vertices of the simplex that are allowed to be in the same face Fi. A graph with the same vertex set as the simplex, and with two vertices adjacent if they...

A local criterion for Tverberg graphs

The topological Tverberg theorem states that for any prime power q and continuous map from a (d+ 1)(q− 1)-simplex to Rd, there are q disjoint faces Fi of the simplex whose images intersect. It is possible to put conditions on which pairs of vertices of the simplex that are allowed to be in the same face Fi. A graph with the same vertex set as the simplex, and with two vertices adjacent if they ...

On a Topological Generalization of a Theorem of Tverberg