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 ri in this conjecture are powers of the same prime. We also prove some results on common transversals that generalize the classical nonembeddability theorems. W...

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Bibliographic Details
Published in:Discrete & computational geometry 2007-10, Vol.38 (3), p.513-525
Main Author: Karasev, Roman N.
Format: Article
Language:English
Subjects:
Geometry
Mathematics
Theorems
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Summary: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. [PUBLICATION ABSTRACT]
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-007-1355-2