Local criteria for triangulation of manifolds
Leibniz International Proceedings in Informatics, LIPIcs
We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or even an explicit metric on M. No Delaunay property of A is assumed. The result provides a triangulation guarantee for algorithms that construct a simplicial complex by working in local coordinate patches. Because the criteria are easily verified in such a setting, they are expected to be of general use.
Boissonnat, Jean Daniel; Dyer, Ramsay; Ghosh, Arijit; and Wintraecken, Mathijs, "Local criteria for triangulation of manifolds" (2018). Conference Articles. 88.