12 citations · 32 across the 8 of their papers we have counts for
10 papers
Beyond the Borsuk-Ulam theorem: The topological Tverberg story
Pavle V. M. Blagojević, Günter M. Ziegler
Bárány's "topological Tverberg conjecture" from 1976 states that any continuous map of an -simplex to , for , maps points from disjoint f…
The topological transversal Tverberg theorem plus constraints
Pavle V. M. Blagojević, Aleksandra S. Dimitrijević Blagojević, Günter M. Ziegler
In this paper we use the strength of the constraint method in combination with a generalized Borsuk-Ulam type theorem and a cohomological intersection lemma to show how one can obt…
Six topics on inscribable polytopes
Arnau Padrol, Günter M. Ziegler
Inscribability of polytopes is a classic subject but also a lively research area nowadays. We illustrate this with a selection of well-known results and recent developments on six…
Spaces of convex n-partitions
Emerson León, Günter M. Ziegler
We construct and study the space C(\R^d,n) of all partitions of \R^d into n non-empty open convex regions (n-partitions). A representation on the upper hemisphere of an n-sphere is…
Topology of the Grünbaum-Hadwiger-Ramos hyperplane mass partition problem
Pavle V. M. Blagojevic, Florian Frick, Albert Haase +1
In 1960 Grünbaum asked whether for any finite mass in there are hyperplanes that cut it into equal parts. This was proved by Hadwiger (1966) for , b…
On complex highly regular embeddings and the extended Vassiliev conjecture
Pavle V. M. Blagojević, Frederick R. Cohen, Wolfgang Lück +1
A continuous map C^d -> C^N is a complex k-regular embedding if any k pairwise distinct points in C^d are mapped by f into k complex linearly independent vectors in C^N. Our centra…
Unimodular triangulations of dilated 3-polytopes
Francisco Santos, Günter M. Ziegler
A seminal result in the theory of toric varieties, due to Knudsen, Mumford and Waterman (1973), asserts that for every lattice polytope there is a positive integer such tha…
Inscribable stacked polytopes
Bernd Gonska, Günter M. Ziegler
We characterize the combinatorial types of stacked d-polytopes that are inscribable. Equivalently, we identify the triangulations of a simplex by stellar subdivisions that can be r…
A tight colored Tverberg theorem for maps to manifolds
Pavle V. M. Blagojević, Benjamin Matschke, Günter M. Ziegler
We prove that any continuous map of an N-dimensional simplex Delta_N with colored vertices to a d-dimensional manifold M must map r points from disjoint rainbow faces of Delta_N to…
The ideal-valued index for a dihedral group action, and mass partition by two hyperplanes
Pavle V. M. Blagojević, Günter M. Ziegler
We compute the complete Fadell-Husseini index of the 8 element dihedral group D_8 acting on S^d \times S^d, both for F_2 and for integer coefficients. This establishes the complete…