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arXiv · 1803.07642

Local criteria for triangulation of manifolds

Jean-Daniel Boissonnat·Ramsay Dyer·Arijit Ghosh·Mathijs Wintraecken
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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. 2018-03-20. Local criteria for triangulation of manifolds. https://arxiv.org/abs/1803.07642

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