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arXiv · 1608.02140

Mogami manifolds, nuclei, and 3D simplicial gravity

Bruno Benedetti
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Abstract

Mogami introduced in 1995 a large class of triangulated 3-dimensional pseudomanifolds, henceforth called "Mogami pseudomanifolds". He proved an exponential bound for the size of this class in terms of the number of tetrahedra. The question of whether all 3-balls are Mogami has remained open since, a positive answer would imply a much-desired exponential upper bound for the total number of 3-balls (and 3-spheres) with N tetrahedra. Here we provide a negative answer: many 3-balls are not Mogami. On the way to this result, we characterize the Mogami property in terms of nuclei, in the sense of Collet-Eckmann-Younan: "The only three-dimensional Mogami nucleus is the tetrahedron".

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Bruno Benedetti. 2016-08-06. Mogami manifolds, nuclei, and 3D simplicial gravity. https://doi.org/10.1016/j.nuclphysb.2017.04.001

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