Persistent Homology — a Survey

@inproceedings{EdelsbrunnerPersistentH,
  title={Persistent Homology — a Survey},
  author={Herbert Edelsbrunner and John Harer}
}
Persistent homology is an algebraic tool for measuring topological features of shapes and functions. It casts the multi-scale organization we frequently observe in nature into a mathematical formalism. Here we give a record of the short history of persistent homology and present its basic concepts. Besides the mathematics we focus on algorithms and mention the various connections to applications, including to biomolecules, biological networks, data analysis, and geometric modeling. 
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Persistent homology analysis of phase transitions.
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