Triangulating submanifolds: An elementary and quantified version of Whitney’s method

Trianguler les sous-variétés: une version élémentaire et quantifiée de la méthode de Whitney

Jean-Daniel Boissonnat (1) , Siargey Kachanovich (1) , Mathijs Wintraecken (2)

1 DATASHAPE - Understanding the Shape of Data
2 IST Austria - Institute of Science and Technology [Klosterneuburg, Austria]

We quantize Whitney's construction to prove the existence of a triangulation for any C^2 manifold, so that we get an algorithm with explicit bounds. We also give a new elementary proof, which is completely geometric.

Mots clés: Triangulations; Manifolds; Coxeter triangulations

Domaines: Géométrie algorithmique [cs.CG]; Algorithme et structure de données [cs.DS]; Topologie algébrique [math.AT]; Topologie géométrique [math.GT]

Jean-Daniel Boissonnat, Siargey Kachanovich, Mathijs Wintraecken. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete and Computational Geometry, 2020, ⟨10.1007/s00454-020-00250-8⟩. ⟨hal-03109814⟩