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Discrete & Computational Geometry

, Volume 38, Issue 3, pp 513–525 | Cite as

Tverberg's Transversal Conjecture and Analogues of Nonembeddability Theorems for Transversals

  • Roman N. Karasev
Article

Abstract

In this paper we prove a special case of the transversal conjecture of Tverberg and Vrecica. We consider the case when the numbers of parts ri in this conjecture are powers of the same prime. We also prove some results on common transversals that generalize the classical nonembeddability theorems. We also prove an analogue of the colored Tverberg's theorem by Zivaljevic and Vrecica. Instead of multicolor simplices with a common point it gives multicolor simplices with a common m-transversal.

Keywords

Vector Bundle Simplicial Complex Discrete Comput Geom Euler Class Grassmann Variety 
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Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Department of Mathematics, Moscow Institute of Physics and Technology, Institutskiy per. 9DolgoprudnyRussia 141700

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