3 papers
math.AT2025
Grothendieck Topologies and Sheaf Theory for Data and Graphs: An Approach Through Cech Closure Spaces
Antonio Rieser
We initiate the study of sheaves on Cech closure spaces, providing a new, unified approach to sheaf theory on many of the major classes of spaces of interest to applications: topol…
math.AT2024
Semi-coarse Spaces, Homotopy and Homology
Antonio Rieser, Jonathan Treviño-MarroquÃn
We begin the study the algebraic topology of semi-coarse spaces, which are generalizations of coarse spaces that enable one to endow non-trivial `coarse-like' structures to compact…
math.CO2024
A New Construction of the Vietoris-Rips Complex
Antonio Rieser
We present a new, inductive construction of the Vietoris-Rips complex, in which we take advantage of a small amount of unexploited combinatorial structure in the -skeleton of th…