  We apply the recently suggested strategy to lift state spaces and operators
for (2+1)-dimensional topological quantum field theories to state spaces and
operators for a (3+1)-dimensional TQFT with defects. We start from the
(2+1)-dimensional Turaev-Viro theory and obtain a state space, consistent with
the state space expected from the Crane-Yetter model with line defects. This
work has important applications for quantum gravity as well as the theory of
topological phases in (3+1) dimensions. It provides a self-dual quantum
geometry realization based on a vacuum state peaked on a homogeneously curved
geometry. The state spaces and operators we construct here provide also an
improved version of the Walker-Wang model, and simplify its analysis
considerably. We in particular show that the fusion bases of the
(2+1)-dimensional theory lead to a rich set of bases for the (3+1)-dimensional
theory. This includes a quantum deformed spin network basis, which in a loop
quantum gravity context diagonalizes spatial geometry operators. We also obtain
a dual curvature basis, that diagonalizes the Walker-Wang Hamiltonian.
Furthermore, the construction presented here can be generalized to provide
state spaces for the recently introduced dichromatic four-dimensional manifold
invariants.
