The Topological Tverberg Problem and winding numbers
| dc.creator | Schöneborn, Torsten | |
| dc.creator | Ziegler, Günter M. | |
| dc.date | 2004-09-06 | |
| dc.date | 2005-01-24 | |
| dc.date.accessioned | 2026-07-07T05:11:50Z | |
| dc.date.available | 2026-07-07T05:11:50Z | |
| dc.description | 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 partitions'' arise if and only if there are ``many q-winding partitions.'' The d=2 case of the Winding Number Conjecture is a problem about drawings of the complete graphs K_{3q-2} in the plane. We investigate graphs that are minimal with respect to the winding number condition. | |
| dc.description | 19 pages. J. Combinatorial Theory, Ser. A, to appear | |
| dc.identifier | https://arxiv.org/abs/math/0409081 | |
| dc.identifier | http://arxiv.org/abs/math/0409081 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72376 | |
| dc.subject | Combinatorics | |
| dc.subject | Metric Geometry | |
| dc.subject | 052A35, 5A35; 05C62, 55M20 | |
| dc.title | The Topological Tverberg Problem and winding numbers | |
| dc.type | text |