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arXiv · 1905.07715

Plus minus analogues for affine Tverberg type results

Pavle V. M. Blagojevic·Günter M. Ziegler
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Abstract

The classical 1966 theorem of Tverberg with its numerous variations was and still is a motivating force behind many important developments in convex and computational geometry as well as the testing ground for methods from equivariant algebraic topology. In 2018, B\'ar\'any and Sober\'on presented a new variation, the "Tverberg plus minus theorem." In this paper, we give a new proof of the Tverberg plus minus theorem, by using a projective transformation. The same tool allows us to derive plus minus analogues of all known affine Tverberg type results. In particular, we prove a plus minus analogue of the optimal colored Tverberg theorem.

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Pavle V. M. Blagojevic, Günter M. Ziegler. 2019-05-19. Plus minus analogues for affine Tverberg type results. https://arxiv.org/abs/1905.07715

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