Atoms, Nuclei, and 3d Triangulations

Jean-Pierre Eckman , University of Geneva
Jadwin Hall A06

Based on the work of Durhuus-Jonsson and Benedetti-Ziegler, we revisit the question of the number of triangulations of the 3-ball. We introduce a notion of nucleus (a triangulation of the 3-ball without internal nodes, and with each internal face having at most 1 external edge). We show that every triangulation can be built from trees of nuclei. This leads to a new reformulation of Gromov's question: We show that if the number of rooted nuclei with N tetrahedra is exponentially bounded in N, then the number of rooted triangulations with N tetrahedra is also exponentially bounded. This is joint work with Pierre Collet and Maher Younan.