Line and surface defects in Reshetikhin–Turaev TQFT

A modular tensor category C gives rise to a Reshetikhin–Turaev type topological quantum field theory which is defined on 3-dimensional bordisms with embedded C -coloured ribbon graphs. We extend this construction to include bordisms with surface defects which in turn can meet along line defects. The surface defects are labelled by Δ -separable symmetric Frobenius algebras and the line defects by “multi-modules” which are equivariant with respect to a cyclic group action. Our invariant cannot distinguish non-isotopic embeddings of 2-spheres, but we give an example where it distinguishes non-isotopic embeddings of 2-tori.