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Communication Dans Un Congrès Année : 2021

Completions, Perforations and Fillings

Résumé

We introduce new local operations, perforations and fillings, which transform couples of objects (X, Y) such that X is a subset of Y. We complement these two operations by collapses and anti-collapses of both X and Y. This set of operations may be seen as a generalization of transformations based solely on collapses, thus a generalization of simple homotopy. Though these transformations do not, in general, preserve homotopy, we make a link between perforations, fillings, and simple homotopy. We give a full characterization of the collection of couples of objects that is closed under the above set of operations. Also, we provide a full characterization of the collection of couples of objects that is closed under the single operation of collapse.
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Dates et versions

hal-04492844 , version 1 (07-03-2024)

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Gilles Bertrand. Completions, Perforations and Fillings. DGMM 2021: Discrete Geometry and Mathematical Morphology, May 2021, Uppsala, Sweden. pp.137-151, ⟨10.1007/978-3-030-76657-3_9⟩. ⟨hal-04492844⟩
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