43 citations · 163 across the 27 of their papers we have counts for
6 papers · 1 filter
Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes
Henry Adams, Johnathan Bush, Nate Clause +13
We explore emerging relationships between the Gromov--Hausdorff distance, Borsuk--Ulam theorems, and Vietoris--Rips simplicial complexes. The Gromov--Hausdorff distance between two…
Vietoris thickenings and complexes have isomorphic homotopy groups
Henry Adams, Florian Frick, Žiga Virk
We study the relationship between metric thickenings and simplicial complexes associated to coverings of metric spaces. Let be a cover of a separable metric space …
What can you draw?
Florian Frick, Fei Peng
We address the problem of which planar sets can be drawn with a pencil and eraser. The pencil draws any union of black open unit disks in the plane . The eraser produ…
Barycenters of points in polytope skeleta
Michael Gene Dobbins, Florian Frick
The first author showed that for a given point in an -polytope there are points in the -faces of , whose barycenter is . We show that we can increase the d…
Splitting loops and necklaces: Variants of the square peg problem
Jai Aslam, Shujian Chen, Florian Frick +3
Toeplitz conjectured that any simple planar loop inscribes a square. Here we prove variants of Toeplitz' square peg problem. We prove Hadwiger's 1971 conjecture that any simple loo…
Metric reconstruction via optimal transport
Michal Adamaszek, Henry Adams, Florian Frick
Given a sample of points in a metric space and a scale , the Vietoris-Rips simplicial complex is a standard construction to attempt to recover f…