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Article Dans Une Revue Journal of Applied and Computational Topology Année : 2021

Computing persistent Stiefel-Whitney classes of line bundles

Résumé

We propose a definition of persistent Stiefel-Whitney classes of vector bundle filtrations. It relies on seeing vector bundles as subsets of some Euclidean spaces. The usual Čech filtration of such a subset can be endowed with a vector bundle structure, that we call a Čech bundle filtration. We show that this construction is stable and consistent. When the dataset is a finite sample of a line bundle, we implement an effective algorithm to compute its persistent Stiefel-Whitney classes. In order to use simplicial approximation techniques in practice, we develop a notion of weak simplicial approximation. As a theoretical example, we give an in-depth study of the normal bundle of the circle, which reduces to understanding the persistent cohomology of the torus knot (1,2).
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Dates et versions

hal-02619607 , version 1 (25-05-2020)
hal-02619607 , version 2 (11-11-2021)

Identifiants

Citer

Raphaël Tinarrage. Computing persistent Stiefel-Whitney classes of line bundles. Journal of Applied and Computational Topology, 2021, ⟨10.1007/s41468-021-00080-4⟩. ⟨hal-02619607v2⟩
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