20 citations · 41 across the 9 of their papers we have counts for
9 papers
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…
Semi-coarse Spaces, Homotopy and Homology
Antonio Rieser, Jonathan Treviño-Marroquín
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…
Cofibration and Model Category Structures for Discrete and Continuous Homotopy
Antonio Rieser
We show that the categories PsTop and Lim of pseudotopological spaces and limit spaces, respectively, admit cofibration category structures, and that PsTop admits a model category…
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…
Vietoris-Rips Homology Theory for Semi-Uniform Spaces
Antonio Rieser
While the Vietoris-Rips complex is now widely used in both topological data analysis and the theory of hyperbolic groups, many of the fundamental properties of its homology have re…
Cech Closure Spaces: A Unified Framework for Discrete and Continuous Homotopy
Antonio Rieser
Motivated by constructions in topological data analysis and algebraic combinatorics, we study homotopy theory on the category of Cech closure spaces , the category who…
A Topological Approach to Spectral Clustering
Antonio Rieser
We propose two related unsupervised clustering algorithms which, for input, take data assumed to be sampled from a uniform distribution supported on a metric space , and output…
Coisotropic Hofer-Zehnder capacities and non-squeezing for relative embeddings
Samuel Lisi, Antonio Rieser
We introduce the notion of a symplectic capacity relative to a coisotropic submanifold of a symplectic manifold, and we construct two examples of such capacities through modificati…
Lagrangian blow-ups, blow-downs, and applications to real packing
Antonio Rieser
Given a symplectic manifold (M, ω) and a Lagrangian submanifold L, we construct versions of the symplectic blow-up and blow-down which are defined relative to L. Furthermore, we sh…