A Brief History of Persistence
Jose A. Perea
TL;DR
This paper provides a concise overview of the development of persistent homology, tracing its evolution from computational origins to modern categorical and representation-theoretic perspectives.
Contribution
It offers a historical survey highlighting key ideas and advancements in persistent homology over the past two decades.
Findings
Historical progression of persistent homology
Transition from computational to categorical frameworks
Modern theoretical perspectives in the field
Abstract
Persistent homology is currently one of the more widely known tools from computational topology and topological data analysis. We present in this note a brief survey on the evolution of the subject. The goal is to highlight the main ideas, starting from the subject's computational inception more than 20 years ago, to the more modern categorical and representation-theoretic point of view.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology · Advanced Neuroimaging Techniques and Applications