Mogami manifolds, nuclei, and 3D simplicial gravity
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...
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| Format: | Article |
| Language: | English |
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Elsevier
2017-06-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321317301220 |
| Summary: | 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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| ISSN: | 0550-3213 1873-1562 |