Filling Radius and Persistent Homology

Abstract: In this talk, we discuss interesting relations between notions from applied topology and metric geometry in point cloud setting. First, we introduce several notions in both fields to measure the size of a manifold. Then, for a point cloud X in R^n, we relate the life spans of the topological features to their extrinsic and Gromov’s filling radius in R^n, and by using this relation, we give bounds for them with Urysohn width. Next, we discuss an interesting relationship between the life spans of the topological features in PD_k(X) in R^n and l^\infty principal components (PCA_\infty) of the point cloud X.

algebraic topologycategory theory

Audience: researchers in the topic

Bilkent Topology Seminar

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Recordings of talks available at www.youtube.com/channel/UCLrmyGpqxyeVpTcA1b5HcMw/videos