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Mogami triangulations

Geometric and topological combinatorics: Modern techniques and methods October 09, 2017 - October 13, 2017

October 10, 2017 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Bruno Benedetti (University of Miami)
Location: MSRI: Simons Auditorium
  • Local constructions

  • Shellability

  • Triangulations

  • Manifolds

  • Asymptotic enumerations

  • Number of 3-spheres

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



Starting with a tree of tetrahedra, suppose that you are allowed to recursively glue together two boundary triangles that have nonempty intersection.

You may perform this type of move as many times you want. Let us call "Mogami manifolds" the triangulated 3-manifolds (with or without boundary) that can be obtained this way. Mogami, a quantum physicist, conjectured in 1995 that all triangulated 3-balls are Mogami. This conjecture implied a much more important one, namely, that "there are only exponentially many triangulation of the 3-sphere with N tetrahedra".

We study this Mogami property in relation other notions, like simply-connectedness, shellability, and collapsibility. With a topological trick we show that Mogami's conjecture is false. The more important conjecture remains unfortunately wide open.

29705?type=thumb Benedetti Notes 1.69 MB application/pdf Download
Video/Audio Files


H.264 Video 7-Benedetti.mp4 124 MB video/mp4 rtsp://videos.msri.org/data/000/029/581/original/7-Benedetti.mp4 Download
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