Factorization Homology and 4D TQFT

TL;DR

This paper extends the framework of topological quantum field theories by constructing a new theory for the 3-2 part of a 4-3-2 TQFT, building on previous work on invariants of 3-manifolds and stringnet models.

Contribution

It introduces a novel construction for the 3-2 component of a 4-3-2 TQFT, generalizing existing invariants and boundary state spaces to higher dimensions.

Findings

Develops a new 3-2 TQFT construction for 4-3-2 theories

Extends invariants from 3-manifolds with corners to higher-dimensional structures

Provides a framework for future exploration of 4D topological invariants

Abstract

In [BK], it is shown that the Turaev-Viro invariants defined for a spherical fusion category $\mathcal{A}$ extends to invariants of 3-manifolds with corners. In [Kir], an equivalent formulation for the 2-1 part of the theory (2-manifolds with boundary) is described 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 in [CY1993].