Extending Persistence Using Poincaré and Lefschetz Duality

@article{CohenSteiner2009ExtendingPU,
  title={Extending Persistence Using Poincar{\'e} and Lefschetz Duality},
  author={David Cohen-Steiner and Herbert Edelsbrunner and John Harer},
  journal={Foundations of Computational Mathematics},
  year={2009},
  volume={9},
  pages={79-103}
}
Persistent homology has proven to be a useful tool in a variety of contexts, including the recognition and measurement of shape characteristics of surfaces in ℝ3. Persistence pairs homology classes that are born and die in a filtration of a topological space, but does not pair its actual homology classes. For the sublevelset filtration of a surface in ℝ3, persistence has been extended to a pairing of essential classes using Reeb graphs. In this paper, we give an algebraic formulation that… 
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