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Communication Dans Un Congrès Année : 2024

Morse frames

Résumé

In the context of discrete Morse theory, we introduce Morse frames, which are maps that associate a set of critical simplexes to all simplexes. The main example of Morse frames are the Morse references. In particular, these Morse references allow computing Morse complexes, an important tool for homology. We highlight the link between Morse references and gradient flows. We also propose a novel presentation of the Annotation algorithm for persistent cohomology, as a variant of a Morse frame. Finally, we propose another construction, that takes advantage of the Morse reference for computing the Betti numbers in mod 2 arithmetic.
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Dates et versions

hal-04217818 , version 1 (11-10-2023)
hal-04217818 , version 2 (03-02-2024)

Identifiants

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Gilles Bertrand, Laurent Najman. Morse frames. International Conference on Discrete Geometry and Mathematical Morphology (DGMM), S. Brunetti; A. Frosini; S. Rinaldi, Apr 2024, Florence, Italy. ⟨hal-04217818v2⟩
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