A Brief History of Persistence
arXiv:1809.03624
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.
References in corpus (9)
- A roadmap for the computation of persistent homology
- The Theory of the Interleaving Distance on Multidimensional Persistence Modules
- Dualities in persistent (co)homology
- Metrics for generalized persistence modules
- Interactive Visualization of 2-D Persistence Modules
- The Vietoris-Rips complexes of a circle
- Algebraic Stability of Zigzag Persistence Modules
- Computing Multidimensional Persistence
- Towards Persistence-Based Reconstruction in Euclidean Spaces
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