Extending Persistence Using Poincaré and Lefschetz Duality
@article{CohenSteiner2009ExtendingPU, title={Extending Persistence Using Poincar{\'e} and Lefschetz Duality}, author={D. Cohen-Steiner and H. Edelsbrunner and J. 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… CONTINUE READING
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