Thin-G Theory and Local Moves for Gems

Abstract

Using the thin presentation of ann-gem, forn=3, 4, we prove that a set of local moves for crystallizations are sufficient in the sense that any two crystallizations inducing the samen-manifold are related by a finite sequence of moves taken from this set. In dimension 3, we apply the moves to prove an identity among quantum 6j-symbols, and we propose a new model for a quantum topological invariant. In dimension 4, we observe that the thin presentation reduces the description of a 4-manifold to a 3-dimensional one.