A universal state sum

Abstract

We define a universal state sum construction which specializes to most previously known state sums (Turaev-Viro, Dijkgraaf-Witten, Crane-Yetter, Douglas-Reutter, Witten-Reshetikhin-Turaev surgery formula, Brown-Arf). The input data for the state sum is an n-category satisfying various conditions, including finiteness, semisimplicity and n-pivotality. From this n-category one constructs an n+1-dimensional TQFT, and applying the TQFT gluing rules to a handle decomposition of an n+1-manifold produces the state sum.