Mogami manifolds, nuclei, and 3D simplicial gravity

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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”.

Original languageEnglish (US)
Pages (from-to)541-559
Number of pages19
JournalNuclear Physics B
Volume919
DOIs
StatePublished - Jun 1 2017

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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