Persistent Homology
Filtrations, persistence diagrams, and stability theorems.
Persistent Homology. Filtrations, persistence diagrams, and stability theorems.
Foundations and canonical references
The standard treatments of persistent homology approach the subject from complementary angles. Edelsbrunner, Computational Topology: An Introduction (2010) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Supporting and adjacent work
A number of supporting contributions sharpen specific aspects of persistent homology or connect it to neighbouring problems. Topology and data (Carlsson, 2009) contributes to this area as one of the supporting references that inform current practice.
Open methodological questions for persistent homology include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2010Computational Topology: An Introductionedelsbrunner-2010, harer-2010
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