4 papers
On colorful generalizations of the Goodman--Pollack transversal problem
Nikola Sadovek
We establish a colorful and, more generally, matroidal solution to the problem of Goodman and Pollack on the existence of an -affine -dimensional transversal to a fa…
Bisections of mass assignments by parallel hyperplanes
Nikola Sadovek, Pablo Soberón
In this paper, we prove a result on the bisection of mass assignments by parallel hyperplanes on Euclidean vector bundles. Our methods consist of the development of a novel lifting…
Complex line fields on almost-complex manifolds
Nikola Sadovek, Baylee Schutte
We study linearly independent complex line fields on almost-complex manifolds, which is a topic of long-standing interest in differential topology and complex geometry. A necessary…
Complex analogues of the Tverberg--Vrećica conjecture and central transversal theorems
Nikola Sadovek, Pablo Soberón
The Tverberg--Vrećica conjecture claims a broad generalization of Tverberg's classical theorem. One of its consequences, the central transversal theorem, extends both the centerpoi…