### 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”.

Original language | English (US) |
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Pages (from-to) | 541-559 |

Number of pages | 19 |

Journal | Nuclear Physics B |

Volume | 919 |

DOIs | |

State | Published - Jun 1 2017 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Mogami manifolds, nuclei, and 3D simplicial gravity.** / Benedetti, Bruno.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 919, pp. 541-559. https://doi.org/10.1016/j.nuclphysb.2017.04.001

}

TY - JOUR

T1 - Mogami manifolds, nuclei, and 3D simplicial gravity

AU - Benedetti, Bruno

PY - 2017/6/1

Y1 - 2017/6/1

N2 - 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”.

AB - 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”.

UR - http://www.scopus.com/inward/record.url?scp=85017395660&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85017395660&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2017.04.001

DO - 10.1016/j.nuclphysb.2017.04.001

M3 - Article

AN - SCOPUS:85017395660

VL - 919

SP - 541

EP - 559

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -