Local criteria for triangulating general manifolds - Boissonnat, Jean-Daniel; Dyer, Ramsay; Ghosh, Arijit; Wintraecken, Mathijs; ISTplus - Postdoctoral Fellowships; Learning and triangulating manifolds via collapses (Discrete & Computational Geometry, 2023)
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.
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Keywords: article; Computational Theory and Mathematics -- Discrete Mathematics and Combinatorics -- Geometry and Topology -- Theoretical Computer Science