5 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…
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--VreÄica conjecture and central transversal theorems
Nikola Sadovek, Pablo Soberón
The Tverberg--VreÄica conjecture claims a broad generalization of Tverberg's classical theorem. One of its consequences, the central transversal theorem, extends both the centerpo…
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…
Convex Equipartitions inspired by the little cubes operad
Pavle V. M. Blagojevic, Nikola Sadovek
A decade ago two groups of authors, Karasev, Hubard and Aronov, and BlagojeviÄ and Ziegler, have shown that the regular convex partitions of a Euclidean space into parts yield…