Local Criteria for Triangulation of Manifolds

Abstract : 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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Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh, Mathijs Wintraecken. Local Criteria for Triangulation of Manifolds. International Symposium on Computational Geometry, Jun 2018, Budapest, Hungary. 2018, 〈10.4230/LIPIcs.SoCG.2018.9〉. 〈hal-01801616〉

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