Computing persistent Stiefel–Whitney classes of line bundles

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