A number of important results in combinatorics, discrete geometry, and theoretical computer
science have been proved using algebraic topology. While the results are quite famous …

Topology of the Grünbaum–Hadwiger–Ramos hyperplane mass partition problem Page 1
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 370, Number 10 …

Mass partition problems describe the partitions we can induce on a family of measures or
finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In this …

Following ideas of Iriyeh and Shibata we give a short proof of the three-dimensional Mahler
conjecture for symmetric convex bodies. Our contributions include, in particular, simple self …

This survey is devoted to some results in the area of combinatorial and convex geometry,
from classical theorems up to the latest contemporary results, mainly those results whose …

We treat problems of fair division, their various interconnections, and their relations to
Sperner's lemma and the Knaster--Kuratowski--Mazurkiewicz (KKM) theorem as well as their …

We compute the complete Fadell–Husseini index of the dihedral group D 8=(Z 2) 2⋊ Z 2
acting on S d× S d for F 2 and for Z coefficients, that is, the kernels of the maps in equivariant …

The well-known “splitting necklace theorem” of Alon [N. Alon, Splitting necklaces, Adv. Math.
63 (1987) 247–253] says that each necklace with k⋅ ai beads of color i= 1,…, n, can be fairly …

Hyperplane Mass Partitions via Relative Equivariant Obstruction Theory Page 1 Documenta
Math. 735 Hyperplane Mass Partitions via Relative Equivariant Obstruction Theory Pavle VM …

A significant group of problems coming from the realm of combinatorial geometry can be
approached fruitfully through the use of Algebraic Topology. From the first such application …