1 research outputs found
Tverberg plus constraints
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.Comment: 15 pages; revised version, accepted for publication in Bulletin
London Math. Societ