Local Criteria for Triangulation of Manifolds
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.
manifold
simplicial complex
homeomorphism
triangulation
9:1-9:14
Regular Paper
Jean-Daniel
Boissonnat
Jean-Daniel Boissonnat
Ramsay
Dyer
Ramsay Dyer
Arijit
Ghosh
Arijit Ghosh
Mathijs
Wintraecken
Mathijs Wintraecken
10.4230/LIPIcs.SoCG.2018.9
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