7 research outputs found
Tverberg's Theorem at 50: Extensions and Counterexamples
We describe how a powerful new “constraint
method” yields many different extensions of the topological
version of Tverberg’s 1966 Theorem in the prime power case—
and how the same method also was instrumental in the recent
spectacular construction of counterexamples for the general
case
Projective center point and Tverberg theorems
We present projective versions of the center point theorem and Tverberg's
theorem, interpolating between the original and the so-called "dual" center
point and Tverberg theorems.
Furthermore we give a common generalization of these and many other known
(transversal, constraint, dual, and colorful) Tverberg type results in a single
theorem, as well as some essentially new results about partitioning measures in
projective space.Comment: 10 page