Plus Minus Analogues for Affine Tverberg Type Results

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 a testing ground for methods from equivariant algebraic topology. In 2018, Bárány and Soberón 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.