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Communication Dans Un Congrès Année : 2024

Morse sequences

Résumé

We introduce the notion of a Morse sequence, which provides a simple and effective approach to discrete Morse theory. A Morse sequence is a sequence composed solely of two elementary operations, that is, expansions (the inverse of a collapse), and fillings (the inverse of a perforation). We show that a Morse sequence may be seen as an alternative way to represent the gradient vector field of an arbitrary discrete Morse function. We also show that it is possible, in a straightforward manner, to make a link between Morse sequences and different kinds of Morse functions. At last, we introduce maximal Morse sequences, which formalize two basic schemes for building a Morse sequence from an arbitrary simplicial complex.
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Dates et versions

hal-04227281 , version 1 (03-10-2023)
hal-04227281 , version 2 (11-10-2023)
hal-04227281 , version 3 (09-02-2024)

Identifiants

  • HAL Id : hal-04227281 , version 3

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Gilles Bertrand. Morse sequences. International Conference on Discrete Geometry and Mathematical Morphology (DGMM), Apr 2024, Florence, Italy. ⟨hal-04227281v3⟩
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