# The Topological Tverberg Problem and winding numbers

@article{Schoneborn2004TheTT, title={The Topological Tverberg Problem and winding numbers}, author={Torsten Schoneborn and G{\"u}nter M. Ziegler}, journal={arXiv: Combinatorics}, year={2004} }

The Topological Tverberg Theorem claims that any continuous map of a (q-1)(d+1)-simplex to \R^d identifies points from q disjoint faces. (This has been proved for affine maps, for d=1, and if q is a prime power, but not yet in general.) The Topological Tverberg Theorem can be restricted to maps of the d-skeleton of the simplex. We further show that it is equivalent to a ``Winding Number Conjecture'' that concerns only maps of the (d-1)-skeleton of a (q-1)(d+1)-simplex to \R^d. ``Many Tverberg…

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