منابع مشابه
The Triangulation of Manifolds
A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the questions. MR classifications 57Q15, 01A60, 57R58.
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We present an algorithmic framework for producing Delaunay triangulations of manifolds. The input to the algorithm is a set of sample points together with coordinate patches indexed by those points. The transition functions between nearby coordinate patches are required to be bi-Lipschitz with a constant close to 1. The primary novelty of the framework is that it can accommodate abstract manifo...
متن کاملLocal 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 ...
متن کاملSimplicial Manifolds, Bistellar Flips and a 16-Vertex Triangulation of the Poincaré Homology 3-Sphere
We present an algorithm based on bistellar operations that provides a useful tool for the construction of simplicial manifolds with few vertices. As an example, we obtain a 16-vertex triangulation of the Poincar e homology 3-sphere; we construct an innnite series of non-P L d-dimensional spheres with d+13 vertices for d 5; and we show that if a d-manifold admits any triangulation on n vertices,...
متن کاملSimplicial Triangulation of Noncombinatorial Manifolds of Dimension Less than 9
Necessary and sufficient conditions are given for the simplicial triangulation of all noncombinatorial manifolds in the dimension range 5 < n < 7, for which the integral Bockstein of the combinatorial triangulation obstruction is trivial. A weaker theorem is proven in case n = 8. The appendix contains a proof that a map between PL manifolds which is a TOP fiber bundle can be made a PL fiber bun...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 1976
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmath/27.1.63