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

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 r_i 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.

Authors and Affiliations

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

   Roman N. Karasev

Corresponding author

Correspondence to Roman N. Karasev.

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