Henry Adams - Vietoris-Rips Complexes of Hypercube Graphs
Explore Vietoris-Rips complexes of hypercube graphs, their homotopy types, and applications in genetic recombination and persistent homology. Discover formulas, open questions, and conjectures in this fascinating area of applied algebraic topology.
Star Clusters in Clique Complexes and the Vietoris-Rips Complex of Planar Sets
Explore star clusters in simplicial complexes and their applications to independence complexes and Vietoris-Rips complexes of planar sets, with insights on homotopy information and related conjectures.
Vietoris-Rips Complexes of Hypercube Graphs
Explore Vietoris-Rips complexes of hypercube graphs, their collapsibility, and applications in genetic trees and persistent homology. Gain insights into simplicial complexes and topological data analysis.
Homotopical Decompositions of Simplicial and Vietoris Rips Complexes
Explore homotopical decompositions of simplicial complexes, focusing on obstruction complexes and their applications in topological data analysis, with insights on Vietoris-Rips complexes.
The Vietoris Rips Complex of the Circle
Explore the Vietoris-Rips complex of the circle, its homotopy types at different thresholds, and implications for persistent homology in topological data analysis.
Bridging Applied and Quantitative Topology
Survey of emerging connections between applied and quantitative topology, focusing on Vietoris-Rips complexes and their applications in computational topology, geometric group theory, and dataset shape approximation.
Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius
Explore geometric persistent homology, its isomorphism with Vietoris-Rips filtration, and applications in characterizing persistence barcodes, bounding intervals, and connecting to filling radius.
Vietoris-Rips Thickenings - Problems for Birds and Frogs
Explore open problems in Vietoris-Rips complexes, connecting diverse mathematical areas. Suitable for both broad theorists and problem-solving specialists in applied algebraic topology.
Decomposing Simplicial Complexes - Without Losing Pieces
Explore simplicial complex decomposition, its impact on homotopy type, and applications in Vietoris-Rips complexes. Learn about obstruction complexes and their role in understanding topological changes.
Andrew Thomas - Functional Limit Theorems for Euler Characteristic Processes
Explore functional limit theorems for Euler characteristic processes in Vietoris-Rips complexes, covering strong law of large numbers and central limit theorem in the thermodynamic regime.
Johnathan Bush - Maps of Čech and Vietoris–Rips Complexes into Euclidean Spaces
Explore simplex-preserving maps in Čech and Vietoris–Rips complexes, their applications, and the challenge of finding such maps from various domains to Euclidean spaces.
Ulrich Bauer - Gromov Hyperbolicity, Geodesic Defect, and Apparent Pairs in Rips Filtrations
Explore Gromov hyperbolicity, geodesic defect, and apparent pairs in Rips filtrations, extending Rips' results on contractibility and examining computational implications for persistent homology.
Vietoris-Rips Complexes and Geometric Group Theory
Explore Vietoris-Rips complexes in geometric group theory, focusing on topological finiteness properties, hyperbolic groups, and recent developments in Morse theory and persistent homology.
Homotopy Types of Vietoris–Rips Complexes of Metric Gluings
Explore homotopy types of Vietoris-Rips complexes in metric wedge sums and gluings, with applications to persistent homology of metric graphs and insights into open research directions.
A Counter-Example to Hausmann's Conjecture
Explore a counter-example to Hausmann's conjecture on Vietoris-Rips complexes, challenging long-held beliefs in algebraic topology using persistent homology.
Gromov-Hausdorff Distances, Borsuk-Ulam Theorems, and Vietoris-Rips Complexes
Explore Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes in geometry. Learn about recent advancements in lower bounding distances between spheres using innovative mathematical techniques.
Some Remarks on the Cohomology of the Vietoris-Rips Complex of a Hypercube Graph
Explore advanced algebraic topology concepts, focusing on the cohomology of Vietoris-Rips complexes in hypercube graphs, with insights from expert Martin Bendersky.