# 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={133-134}
}
• Published 23 January 2009
• Mathematics
• Foundations of Computational Mathematics
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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