A G -Equivariant String-Net Construction

We develop a string-net construction for the (2,1)-dimensional part of a G -equivariant three-dimensional topological field theory based on a G -graded spherical fusion category. In this construction, a G -equivariant generalization of the Ptolemy groupoid enters. We compute the associated cylinder categories and show that, as expected, the model is closely related to the G -equivariant Turaev–Viro theory.