Topology Seminar (Main Talk): Local constructions of triangulated manifolds.

Seminar | September 6 | 4-5 p.m. | 3 Evans Hall

 Bruno Benedetti, University of Miami

 Department of Mathematics

A "tree of tetrahedra” is a simplicial complex that is homeomorphic to the 3-ball and that has a tree as dual graph. Starting with a tree of tetrahedra, suppose that you are allowed to recursively glue together two *incident* boundary triangles. (You can perform this type of move as many times you want.) Call "Mogami manifolds" the triangulated 3-manifolds that you can obtain this way. Are all triangulated 3-balls Mogami?

This question, originally asked in a 1995 quantum physics paper, turns out to be related to known topological and combinatorial properties, like simply-connectedness and shellability. A "yes" answer would imply a much desired result in combinatorics, namely, that there are only exponentially many triangulated 3-balls. Using elementary knot theory, we show that unfortunately the answer is "no".