Tverberg plus constraints

Abstract

Many of the strengthenings and extensions of the topological Tverberg theorem can be derived with surprising ease directly from the original theorem: For this we introduce a proof technique that combines a concept of "Tverberg unavoidable subcomplexes" with the observation that Tverberg points that equalize the distance from such a subcomplex can be obtained from maps to an extended target space. Thus we obtain simple proofs for many variants of the topological Tverberg theorem, such as the colored Tverberg theorem of Zivaljevic and Vrecica (1992). We also get a new strengthened version of the generalized van Kampen-Flores theorem by Sarkaria (1991) and Volovikov (1996), an affine version of their "j-wise disjoint" Tverberg theorem, and a topological version of Soberon's (2013) result on Tverberg points with equal barycentric coordinates.

15 pages; revised version, accepted for publication in Bulletin London Math. Society

Cited by in corpus (6)

• Eliminating Higher-Multiplicity Intersections, III. Codimension 2
• Invariants of graph drawings in the plane
• Average-Value Tverberg Partitions via Finite Fourier Analysis
• Hyperplane Equipartitions Plus Constraints
• Regular Polygonal Partitions of a Tverberg Type
• Stronger counterexamples to the topological Tverberg conjecture