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The Vietoris Rips Complex of the Circle

Offered By: Applied Algebraic Topology Network via YouTube

Tags

Vietoris-Rips Complexes Courses Homotopy Courses Persistent Homology Courses Applied Algebraic Topology Courses

Course Description

Overview

Explore the Vietoris-Rips complex of the circle in this 57-minute lecture from the Applied Algebraic Topology Network. Delve into the behavior of Vietoris-Rips complexes for varying distance thresholds, starting with Jean-Claude Hausmann's theorem on small thresholds for Riemannian manifolds. Discover how the homotopy type of the Vietoris-Rips complex of the circle evolves as the distance threshold increases, progressing through various spheres before becoming contractible. Learn about the applications of these complexes in persistent homology and gain insights from the joint work with Michal Adamaszek. Access accompanying slides for visual support of the concepts presented.

Syllabus

Henry Adams (3/3/15): The Vietoris Rips Complex of the Circle


Taught by

Applied Algebraic Topology Network

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