14 citations · 55 across the 20 of their papers we have counts for
23 papers
Quantifying discontinuity
Henry Adams, Florian Frick, Michael Harrison +2
Given a compact space that does not admit an embedding (an injective continuous function) into , we study the ''degree'' of discontinuity that any injective funct…
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…
Unit sphere fibrations in Euclidean space
Daniel Asimov, Florian Frick, Michael Harrison +1
We show that if an open set in can be fibered by unit -spheres, then , and if , then the spheres must be pairwise linked, and $n \in \left\…
Tangent ray foliations and their associated outer billiards
Yamile Godoy, Michael Harrison, Marcos Salvai
Let be a unit vector field on a complete, umbilic (but not totally geodesic) hypersurface in a space form; for example on the unit sphere …
Skew and sphere fibrations
Michael Harrison
A great sphere fibration is a sphere bundle with total space and fibers which are great -spheres. Given a smooth great sphere fibration, the central projection to any tang…
SIC-POVMs from Stark units: Prime dimensions n^2+3
Marcus Appleby, Ingemar Bengtsson, Markus Grassl +2
We propose a recipe for constructing a SIC fiducial vector in complex Hilbert space of dimension of the form , focussing on prime dimensions . Such structures are sho…