Persistent Homology and Applied Homotopy Theory
Gunnar Carlsson
TL;DR
This survey reviews persistent homology and applied homotopy theory, covering theoretical foundations, stability results, vectorization techniques, and various applications in topological data analysis.
Contribution
It provides a comprehensive overview of persistent homology, integrating recent theoretical developments and practical applications in topological data analysis.
Findings
Summarizes stability theorems for persistence barcodes
Discusses vectorization methods for persistence barcodes
Highlights applications in data analysis
Abstract
This paper is a survey of persistent homology, primarily as it is used in topological data analysis. It includes the theory of persistence modules, as well as stability theorems for persistence barcodes, generalized persistence, vectorization of persistence barcodes, as well as some applications.
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Taxonomy
TopicsTopological and Geometric Data Analysis