43 citations · 163 across the 27 of their papers we have counts for
6 papers · 1 filter
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\…
On inscribed trapezoids and affinely 3-regular maps
Florian Frick, Michael Harrison
We show that any embedding inscribes a trapezoid or maps three points to a line, where is the smallest power of satisfy…
Coupled embeddability
Florian Frick, Michael Harrison
We introduce the notion of coupled embeddability, defined for maps on products of topological spaces. We use known results for nonsingular biskew and bilinear maps to generate simp…
The topology of projective codes and the distribution of zeros of odd maps
Henry Adams, Johnathan Bush, Florian Frick
We show that the size of codes in projective space controls structural results for zeros of odd maps from spheres to Euclidean space. In fact, this relation is given through the to…
Spaces of embeddings: Nonsingular bilinear maps, chirality, and their generalizations
Florian Frick, Michael Harrison
Given a space X we study the topology of the space of embeddings of X into through the combinatorics of triangulations of X. We give a simple combinatorial formula f…
Metric Thickenings, Borsuk-Ulam Theorems, and Orbitopes
Henry Adams, Johnathan Bush, Florian Frick
Thickenings of a metric space capture local geometric properties of the space. Here we exhibit applications of lower bounding the topology of thickenings of the circle and more gen…