A promising entry into the study of 4-dimensional TQFTs is the definition of state-sum invariants of 4-manifolds by Douglas-Reutter. In it a so-called spherical fusion 2-category is used as an input for a construction, analogous to that of 3-dimensional topological quantum field theories (TQFTs) of Turaev-Viro-Barrett-Westburry type. In dimensions 2 and 3 the state-sum TQFTs have been shown to be instances of generalised orbifolds of defect TQFTs. In fact, the notion of a state-sum TQFT in any dimension is conjecturally analogous to that of a generalised orbifold of the trivial defect TQFT. The aim of this project with Nils Carqueville and Lukas Müller is to demonstrate this in dimension 4, i.e. to formulate the Douglas-Reutter theory as a generalised orbifold. We will also explore how such description can be used to expand the 4-dimensional state-sum construction to include boundary conditions and domain walls, as well as defects of higher codimension.
Duration of stay:
1st October - 31st December 2022
|Vincentas Mulevicius||Max Planck Institute for Mathematics|