43 citations · 163 across the 27 of their papers we have counts for
5 papers · 1 filter
Borsuk-Ulam theorems for products of spheres and Stiefel manifolds revisited
Yu Hin Chan, Shujian Chen, Florian Frick +1
We give a different and possibly more accessible proof of a general Borsuk--Ulam theorem for a product of spheres, originally due to Ramos. That is, we show the non-existence of ce…
On homotopy types of Euclidean Rips complexes
Michal Adamaszek, Florian Frick, Adrien Vakili
The Rips complex at scale r of a set of points X in a metric space is the abstract simplicial complex whose faces are determined by finite subsets of X of diameter less than r. We…
Hyperplane mass partitions via relative equivariant obstruction theory
Pavle V. M. Blagojević, Florian Frick, Albert Haase +1
The Grünbaum-Hadwiger-Ramos hyperplane mass partition problem was introduced by Grünbaum (1960) in a special case and in general form by Ramos (1996). It asks for the "admissible"…
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…
Nerve complexes of circular arcs
Michal Adamaszek, Henry Adams, Florian Frick +2
We show that the nerve complex of n arcs in the circle is homotopy equivalent to either a point, an odd-dimensional sphere, or a wedge sum of spheres of the same even dimension. Mo…