Factorization homology and 4D TQFT

Abstract

In 2010, B. Balsam and A. Kirillov, Jr. showed that the Turaev–Viro invariants defined for a spherical fusion category $\mathcal{A}$ extends to invariants of 3-manifolds with corners. In 2021, A. Kirillov, Jr. described an equivalent formulation for the 2-1 part of the theory (2-manifolds with boundary) using the space of “stringnets with boundary conditions” as the vector spaces associated to 2-manifolds with boundary. Here we construct a similar theory for the 3-2 part of the 4-3-2 theory by L. Crane and D. Yetter (1993).