Combinatorics-Seminar

SPEAKER:  Bruno Benedetti  (University of Miami)

TITLE:  Local constructions of manifolds

ABSTRACT: 

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 implies an important one in discrete quantum gravity (namely, that there are exponentially many triangulations of the 3-ball.) Using a topological trick, we show that Mogami's conjecture is false.