Speaker
Description
We study a generalization of a 4-dimensional BF-theory in the context of higher gauge theory. We have defined the state sum $Z_{3BF}$ that is a topological invariant of 4-dimensional manifolds using the higher categorical structure of a 3-group. The definition of the state sum $Z_{3BF}$ is then extended to a new state sum $Z_\partial$, that corresponds to 4-dimensional manifolds with boundary, and it is demonstrated that this extended definition gives rise to a TQFT, by explicitly verifying the axioms. It is shown that it inherently defines a functor between two dagger symmetric monoidal categories equipped with a dual: the category of 4-dimensional cobordisms between 3-dimensional manifolds and the category of finite-dimensional Hilbert spaces.
