A G-Equivariant String-Net Construction

Abstract

AbstractWe 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.